From around my french table.
This requires an overnight rest, so if you need it sooner, make other plans!
1/4 C warm to the touch whole milk
1/4 C warm to the touch water
3 Tb sugar
4 tsp active dry yeast
2 3/4 flour
1 1/2 tsp salt
3 lg eggs, room temp, lightly beaten
12 Tb butter, room temp
Pour milk and water into the bowl of a stand mixer, add pinch of sugar and sprinkle over the yeast. In antoher bowl mix flour and salt together.
Once yeast has absorbed some liquid, stir with a wooden spoon until mixture is creamy. Load mixer with a dough hook, add all flour at once, and turn on and off for a few short pulses to dampen flour. Set mixer to medium-low and mix for a minute or two, scraping sides/bottom as needed until you have a shaggy, farily dry mass. It will be pretty ugly, but that's ok.
Scrape down bowl, turn on to low, and add beaten eggs one third at a time, beating until incorporated before adding the next third. Beat in remaining sugar, increase seed to medium, and beat for about 3 minutes until dough starts coming together.
Reduce speed to low and add butter in 2Tb chunks. (Can squeeze between fingers to soften as dropping in.) Beat about 30 seconds until almost incorporated before adding the next little piece. When butter is all in, you'll have a soft, batterish dough. Increase speed to med-high and beat until dough pulls away from sides and climbs up the hook, about 10 minutes or a bit longer.
Transfer to lightly buttered bowl, cover with plastic, leave at room temp until nearly doubled, an hour or longer.
Deflate by lifting it up around the edges and letting it fall with a slap. Cover and refrigerate 2 hours, slapping it down every 30 minutes.
Press plastic against surface of dough and leave it to chill overnight.