I am an Italian Noahide who has been attending this great forum for some years. Given that this question concerns us Gentiles, I take the liberty of trying to give my own interpretative answer, even if I realize that I am a mere amateur on the subject.
We read in Rambam's Mishneh Torah-Hilchot Melachim 10: 9-10 (English translation by Rabbi Eliyahu Touger):
"A gentile who studies the Torah is obligated to die. They should only be involved in the study of their seven mitzvot.
Similarly, a gentile who rests, even on a weekday, observing that day as a Sabbath, is obligated to die. Needless to say, he is obligated for that punishment if he creates a festival for himself.
The general principle governing these matters is: They are not to be allowed to originate a new religion or create mitzvot for themselves based on their own decisions. They may either become righteous converts and accept all the mitzvot or retain their statutes without adding or detracting from them.
If a gentile studies the Torah, makes a Sabbath, or creates a religious practice, a Jewish court should beat him, punish him, and inform him that he is obligated to die. However, he is not to be executed.
We should not prevent a gentile who desires to perform one of the Torah's mitzvot in order to receive reward from doing so, provided he performs it as required. If he brings an animal to be sacrificed as a burnt offering, we should receive it."
Now, it is clear to me that the harsh prohibition, foreseen at the beginning of this passage, for the Gentile who studies the Torah, and therefore, by logical consequence, the prohibition for a Jew to teach the Torah to a Gentile,
must be interpreted in the light of what Rambam states in step 10: "We should not prevent a gentile who desires to perform one of the Torah's mitzvot in order to receive reward from doing so, provided he performs it as required ". Question: But how can a Gentile exercise the right to fulfill a Torah mitzva, "it as required", if he does not study it thoroughly first?
Suppose, for example, that an Italian cattle breeder wants, for free choice, to fulfill the mitzva on the kosher slaughter of meat: Rambam tells us that he has the right to do so, but in order to be able to do so, the Gentile must necessarily study what the Torah teaches on the subject, perhaps by consulting the Shulchan Arukh or the Mishneh Torah,
or by asking a rabbi that this precept be explained to him in detail.
It would seem at first glance that there is a contradiction in Rambam's thinking. But in my opinion the harmonizing solution lies in this specific passage:
"The general principle governing these matters is: They are not to be allowed to originate a new religion or create mitzvot for themselves based on their own decisions. They may either become righteous converts and accept all the mitzvot or retain their statutes without adding or detracting from them".
In my opinion, Rambam specifies here that the prohibition for the Gentile to study the Torah is related to the case in which he wants to alter the design that HaShem has established for Jews and Gentiles, creating a "new religion".
In fact, it is one thing that the Gentile fulfills by free choice a precept of the Torah not contained in the Noahide Law, another thing is that a religious faith is created on the basis of which the Gentiles are obliged by HaShem to observe commandments other than the seven precepts, which would go against the teaching of the Torah itself.
I conclude with another reflection: there is also the study of a particular precept of the Torah that a Gentile can appreciate for pure intellectual pleasure; in this case the risk of creating a "new religion" seems to me excluded at the root.