Special equipment: a standing mixer with whisk and dough-hook attachments.
Starter: Stir together sugar and milk in a small bowl. Sprinkle yeast over mix and let stand until foamy, 10 minutes. Stir flour into yeast, forming a soft dough and cut a deep X across the top. Let starter rise, covered with plastic wrap, at room temperature, 1 hour.
Dough: Combine salt, sugar, and hot milk in a small bowl and stir until salt and sugar are dissolved. Fit mixer with whisk attachment, and then beat 2 eggs at medium-low speed until fluffy. Add sugar mixture and beat until combined well. With motor running, add in order, beating after each addition:
About one fourth of butter,
And remaining 1/2 cup flour.
Remove bowl from mixer and fit mixer with dough hook attachment. Spread starter onto dough with a rubber spatula and return bowl to mixer. Beat dough at medium-high speed 6 minutes, or until dough is smooth and elastic. Add remaining butter, cubed and grated cheeses and beat 1 minute, or until butter and cheeses are incorporated.
Lightly butter a large bowl and scrape dough into that bowl with a rubber spatula. Lightly dust dough with flour to prevent crust forming. Cover with plastic wrap and let rise at room temperature until more than doubled in bulk, 2 to 3 hours.
Punch the dough down and lightly dust with flour. Cover, again, with plastic wrap and CHILL dough, punching down after the first hour, at least 12 hours.
Place a pie pan on bottom shelf of oven. Butter muffin tins generously. Take a small lump of dough, dust wit ha little flour and roll in your hands into a ball. Place in muffin tin, dough should come just above rim of muffin tin. Repeat until tins are filled. “Dock” each top with a sharp knife. Cover pan with linen towel and let brioches rise at least 1/2 hour. They will plump up nicely.
Preheat oven to 425 F for at least 15 minutes. *Remember, your pie pan is on the bottom shelf preheating with the oven.
Place the muffin tins on middle shelf of oven and splash about 1/2 cup water into the pie pan on the bottom shelf. This will create steam in the oven to help rise the brioches. Bake at 425 F for 15 – 20 minutes or until brioches are golden brown. Remove to wire racks, let cool completely.