There is a set of three stories in the Talmud (Shabbos 31a) in which a candidate for conversion approaches Shammai with a desire to convert, "but only if..." And after Shammai chases the person away, the person goes to Hillel who does convert them. The most famous of the three is:
מעשה בנכרי אחד שבא לפני שמאי. אמר לו: "גיירני על מנת שתלמדני כל התורה כולה כשאני עומד על רגל אחת." דחפו באמת הבנין שבידו. בא לפני הלל, גייריה. אמר לו: "דעלך סני, לחברך לא תעביד! - זו היא כל התורה כולה, ואידך - פירושה הוא, זיל גמור.
A story about a non-Jew who came before Shammai. [The non-Jew] said to [Shammai], “Convert me on the condition that you teach me the entire Torah while I stand on one foot.” [Shammai] chased him away with the builder’s measuring stick that was in his hand. [The non-Jew] came before Hillel [with the same request] and he converted him. [Hillel] said to him, “That which you loath, do not do to others. That is the whole Torah. Go study!”
According to Hillel, the central principle of the entire Torah is the law of empathy. (To coin a general term for the idea that finds various expressions here, in the Christian Golden Rule, the notion of Karma, etc...) So it would seem that all of Torah unfolds from this kind of Natural Morality.
And so too in the reverse. If there is a dispute over some law in halakhah and a voice from heaven were to declare what the rule would be, we still follow the halachic process rather than the prophetic voice. There is a famous story about this but I will leave it to you to search for "Tanur shel Achnai" and I'll skip right to the prooftext. Devarim 30:11-14:
כִּי הַמִּצְוָה הַזֹּאת אֲשֶׁר אָנֹכִי מְצַוְּךָ הַיּוֹם לֹא-נִפְלֵאת הִוא מִמְּךָ וְלֹא רְחֹקָה הִוא. לֹא בַשָּׁמַיִם הִוא לֵאמֹר, "מִי יַעֲלֶה-לָּנוּ הַשָּׁמַיְמָה וְיִקָּחֶהָ לָּנוּ וְיַשְׁמִעֵנוּ אֹתָהּ וְנַעֲשֶׂנָּה?" וְלֹא-מֵעֵבֶר לַיָּם הִוא לֵאמֹר, "מִי יַעֲבָר-לָנוּ אֶל-עֵבֶר הַיָּם וְיִקָּחֶהָ לָּנוּ, וְיַשְׁמִעֵנוּ אֹתָהּ וְנַעֲשֶׂנָּה?" כִּי-קָרוֹב אֵלֶיךָ הַדָּבָר מְאֹד, בְּפִיךָ וּבִלְבָבְךָ, לַעֲשֹׂתוֹ.
For this commandment that I command you today is not a wonder to you nor is it remote. It is not in the heaven, for you to say, “Who will ascend to heaven for us, and grasp it for us, so that we can hear it and perform it?” And it is not on the other side of the sea, for you to say, “Who will cross the sea for us, and grasp it for us, so that we can hear it and perform it?” Rather, the matter is very close to you, in your mouth and heart, to perform it.
The translation of these verses is an encouraging message that obserrvance is in our reach. However, hermeneutically, "it is not in heaven" is taken to mean that since the Torah was given to us during the Exodus, no more halakhah will be given to us from heaven. But let's look at the rest of the pragraph, the "why" -- "the matter is very close to you, in your mouth and heart, to perform it."
Just as all of halakhah derives from Natural Morality, only a person with Natural Morality, "close... in ... mouth and heart" is empowered to interpret it.
The only problem is that because the Torah's Author is better informed about what the other would loathe in the longest run than we are, halakhah can override a naive Natural Moral decision. (A natural one?) Same motives, different results.
And there are numerous halakhos that presuppose a duty to follow Natural Morality. See Devarim 6:18,"וְעָשִׂ֛יתָ הַיָּשָׁ֥ר וְהַטּ֖וֹב בְּעֵינֵ֣י ה֑׳ לְמַ֙עַן֙ יִ֣יטַב לָ֔ךְ – and you shall do what is the honest and the good in Hashem’s ‘Eyes’, so that He shall benefit to you…” and the Ramban there:
And according to our rabbis, they said about this a beautiful medrash: This is about compromise and staying within the limits of the law. The intent in this is that at that beginning He says that you should observe His statutes and testimonies which He commands, and now it says also about those things he didn’t command – set your mind on doing the right and the honest in His “Eyes” because He Loves the good and the honest.
This is an important topic, because it is impossible for the Torah to mention every activity a person has with his neighbors and friends and all his interactions, all his buying and selling, and the norms of communities and countries. But after it mentions many of them, like “Do not go around as a gossip,” “do not take revenge and do not bear a grudge,” “do not stand by your peer’s blood,” “do not curse the deaf,” “rise up before the elderly” and the like, it returns to say as a general rule that he should to what is good and honest in everything. Until he enters through this into compromise and staying within the limits of the law.
And Rav Shimon Shkop (Shaarei Yosher 5:1) says something similar about the basis of fiscal halakhos in particular:
When we seek to determine the rights or liabilities with respect to asset, we are not engaged in a question relating to the observance of a mitzvah. Instead, we are asking a question regarding ownership on the basis of the rules established by the the rules of justice.
And it is on this basis that the Talmudic rabbis announced the rules that apply when ownership of an asset is in doubt. Certainly it was based on rational discernment that the rules of justice will rule that in a case where a pregnant cow was sold but it was not known whether the calf was born before or after the sale, the calf will belong to the (seller, the) party in possession... And it is clear that the prohibition against theft means that one cannot take property that that the rules of the civil law has assigned to another.
Halakhah presumes Natural Morality as a starting point, and adds to it G-d's more informed perspective and rules for becoming the kinds of people more capable of living up to it. And that is the entire Torah "on one foot."