Kemach and Solet, please explain

Question

See Pirkei Avos- how does a sieve retain the fine flour? for background to this question, reproduced here.
Avos 5(15):

אַרְבַּע מִדּוֹת בְּיוֹשְׁבִים לִפְנֵי חֲכָמִים. סְפוֹג, וּמַשְׁפֵּךְ, מְשַׁמֶּרֶת, וְנָפָה. כו' מְשַׁמֶּרֶת, שֶׁמּוֹצִיאָה אֶת הַיַּיִן וְקוֹלֶטֶת אֶת הַשְּׁמָרִים. וְנָפָה, שֶׁמּוֹצִיאָה אֶת הַקֶּמַח וְקוֹלֶטֶת אֶת הַסֹּלֶת
There are four types among those who sit before the sages: a sponge, a funnel, a strainer and a sieve.... A strainer, which lets out the wine and retains the lees; A sieve, which lets out the kemach and retains the choice flour (סֹּלֶת).

The Rav explains that, unlike the "strainer":

The sieve: After we take out the bran and the bruised grain from the ground flour, the [inferior powdery] flour is left with the coarse fine flour, and [the latter] is the [more] important one; we pass it through a very fine sieve. And all of the [powdery] flour - which is like white dust - falls from it, and the coarse important flour remains. And so would they do with grain offerings.
So [too], there is one who has the ability to separate and to cleanse his teachings and take the truth from the false and wasteful.

You see that the "סולת" required for all the menachos (grain-offerings) in the Torah is the coarse flour. The powdery dust is what you sift out.
We see the same in the mishnah in Menachos, 9(2):

כֵּיצַד הוּא בוֹדֵק. הַגִּזְבָּר מַכְנִיס אֶת יָדוֹ לְתוֹכָהּ. עָלָה בָהּ אָבָק, פְּסוּלָה, עַד שֶׁיְּנִיפֶנָּה
How does the Temple treasurer inspect the flour to determine whether it is of sufficiently high quality? The treasurer inserts his hand into the flour. If, when he removes his hand, flour powder ("dust") covers it, the flour is unfit, until one sifts it with a fine sifter, so that no powder will remain.

Any bakers who could explain this? Do we have this today, "coarse fine flour" and worthless "powdery flour"? Where the "fine flour" wouldn't stick to your hand if you stuck it in? It doesn't seem to fit with my impression of the bags of flour my wife brings home.

Answer 1

Okay! With Kazi bacsi's help (and R' Tzvi Rozen of the Star-K), plus I found a Rashi that addresses this.

1. There is something called "first break", where wheat or grain is not fully ground, but is broken into smaller pieces. In addition to the endosperm, that is the point where you can sift out the shells, the bran, and any other low quality junk "middlings", also see "semolina". It seems complicated.
   That will be the point that the Mishnah in Menachos is describing, where the solet brought in to the treasurer should contain nothing large or small besides endosperm.
   After that you finish grinding it.
   Here's (the early published form of) Rashi at the end of the seventh perek, 76b: https://www.sefaria.org/Menachot.76b.10?lang=bi&with=Rashi&lang2=en

בדקה בגסה - כו'ובתחילה היו מניפין בדקה והיתה קולטת הסלת והסובין והיה הקמח הולך כו' ואח"כ נותנין אותו בגסה שקולטת הסובין שנשתיירו בסלת והגרוסות כעין קרטין שממנו הסלת נעשה היה הולך לעבר הנפה כו' וכן חוזרין חלילה עד שיהא מנופה שלש עשרה פעמים ובלבד שלא ישתייר מן הקמח ומן הסובין עם הסלת וחוזרין וטוחנין קרטין והגרוסות והויין סלת עכ"ל

With fine and coarse sieves... At first they would sift with the fine sieve and it would collect the solet and the bran, and the powder would sift out... Then they would put it in a coarse sieve to screen out the bran, and let through the solet (and) pieces like chunks from which solet is made. Then they would do it again, 13 times... till all the powder and all the bran are gone. Then they go back and grind up the chunks, and that is solet.

Addendum: I’m wondering if this could also help me with a different issue. The mishnah there says that you need more grain to start with for the Shtei Halechem than for the Lechem Hapanim (two סאה per עשרון instead of just one). The reason given in the gemara is that the Shtei Halechem is chadash, Lechem Hapanim is yashan. Rashi says that as a result, the Shtei Halechem will have more סובין. Rambam in פיה"מ explains

אבל לחם הפנים שהוא מחטה שנקצרה זה ימים והיא יבשה כל צרכה ויש בה סלת הרבה בלי ספק

It bothered me: Why would the quantity of solet compared to סובין change as it gets dryer? אם קבלה נקבל, but how does that work? A description of the part that is not semolina endosperm (Wikipedia on “middlings”):

…shorts (making up approximately 12% of the original grain, consisting of fractions of endosperm, bran, and germ with an average particle size of 500-900 microns) and red dog (actually a low-grade flour, making up approximately 3% of the original grain, consisting of fractions of endosperm and bran, with an average particle size of 100-300 microns).

It describes the קמח powder, here called “red dog”. And the “shorts”, much bigger pieces. Both also contain some endosperm.
I wonder if when the Rishonim are talking about “סולת” and “סובין” after grinding, they’re using rough descriptions of the two main large components (along with the “קמח” powder) of what you get after the first break partial grinding process. The part you want, and the part you don’t want. You’re hoping that all the real wheat stays together, and the shells and bran stay together, so you can sift them out. It’s important that they end up different sizes for the sifting; it’s touchy. But some of the pieces containing shells and bran (and powder too) also contain some of the wheat (endosperm), as the article says. That gets lost, sifted out.
Guesswork: It could be that when the kernel is dry, the separation can be cleaner and you end up with a better result, less wheat getting lost. This would need more research.