Poolish:
In a bowl, dissolve the yeast in the water.
Add the flour and mix the ingredients with greased hands until a ball of dough forms.
Cover the bowl with plastic wrap and let the dough rise for 45 minutes in a warm place.
Brioche:
Put the flour in the mixer bowl.
Add the poolish, salt, sugar, milk, honey, and beaten eggs.
Knead for 8 minutes with the hook.
Add the pieces of butter, a few at a time, while continuing to knead.
The kneading can take 15 minutes, until the butter is well incorporated.
The dough will be heavy and soft.
Cover the mixer bowl with plastic wrap and let the dough rise for 2 hours at room temperature, or until it has doubled in volume.
Flatten the dough under the palm of your hand, then refrigerate for at least 4 hours or overnight.
Flatten the dough again under the palm of your hand, then shape it according to the shape of the baking mold.
I used 2 molds of 5 po x 9 po (12.5 cm x 23 cm) here.
Generously butter the molds, then deposit the dough so that it occupies two-thirds of the mold.
Cover with a damp kitchen towel and let rest for about 45 minutes, until the dough has doubled in volume again.
In the middle of this step, preheat the oven to 400 F (200 C).
Brush the top of the dough with melted butter using a brush.
Using a sharp knife, carefully make a small cross-shaped cut in the middle of the dough.
Bake for 25 to 30 minutes, until the surface of the brioche is golden brown or a toothpick inserted into the center comes out clean.
Remove from the oven and let cool on a rack before serving.