In a large mixing bowl, dissolve the yeast in the lukewarm milk. Add a spoonful of sugar and let it sit for about 5 minutes until it becomes frothy.
To the yeast mixture, add the flour, remaining sugar, salt, and eggs. Mix until the dough starts to form.
Gradually add the softened butter in portions, ensuring each is well incorporated into the dough before adding the next. Knead the dough for about 10 minutes until it is smooth and elastic.
First Rise
Place the dough in a greased bowl, cover with a clean kitchen towel, and let it rise in a warm, draft-free area for about 1-2 hours, or until doubled in size.
Shape the Dough:
Once risen, punch down the dough to release excess air. Turn it out onto a lightly floured surface and divide into desired portions for shaping.
Shape each portion into a smooth ball and arrange in a buttered baking dish or on a baking sheet.
Second Rise:
Cover the shaped dough with the towel again and let it rise for another hour, until puffy and nearly doubled.
Bake
Preheat your oven to 375°F (190°C). Bake the brioche for about 25-30 minutes, or until golden brown on top.
Remove from the oven and let cool on a wire rack before serving.