1Pour the warm milk and the active starter into the food processor bowl and mix well with a spoon or a spatula.
2Add the flour, sugar, salt, and vanilla and mix lightly, just enough to incorporate everything.
3Put the bowl into the food processor, with the kneading hook attached, and start kneading. Add the eggs one at a time. Knead for a few minutes until the batter is nicely uniform.
4Start adding the butter, a little bit at a time, kneading after each addition. Use a dough scraper to scrape the sides of the bowl and send the batter and the butter back toward the hook. Knead until the batter is very smooth and shiny.
5Transfer the batter into a buttered or lightly greased bowl, cover with plastic wrap, and let it rise for several hours in a warm spot (3 to 4 hours). The batter should double in volume.
6Lightly punch down the batter and put it into the refrigerator overnight—this step is essential to facilitate the shaping of the batter.
7The next day, turn the batter out onto a lightly floured work surface and divide it into small portions using a pastry cutter. For filled mini brioches, I suggest portions of approximately 90 grams.
8Lightly flatten each piece, put a teaspoon of jam into the hollow, and then close it up again, making a seam to form it into a ball.
9Place in a buttered tray and let rise for a few hours, depending on the room temperature (usually about 2 hours).
10Bake in a preheated oven at about 350°F (180°C) for 20 to 25 minutes for mini brioches. If you are making one large brioche, extend the baking time.