Heat the milk to 110 degrees F. Add to a large bowl along with the 2 tbsp. of sugar and dissolve the yeast in the milk. Add the eggs and extract and whisk.
In a large bowl of a stand mixer with the dough hook, mix the flour, sugar, zest and salt. Add the wet ingredients and mix until incorporated. Add the butter, 1 piece at a time, mixing in between. Remove the dough and knead into a large ball. Place in an oiled bowl, cover and let rise in a draft free place until doubles, about 1-1 1/2 hours.
Punch down dough and remove from the bowl. Divide into 4 equal pieces, weighing if necessary. Divide each quarter into 3 equal pieces. Roll into 3 equal snakes. Attach by pinching the ends of 3 pieces together and braid. Insert colored eggs if using by slipping them into the spaces. Place on sheet pans and cover to let rise an additional 40-45 minutes.
Pre-heat oven to 350 degrees. Uncover and brush with egg wash. Bake in the oven until golden and cooked thoroughly with an internal temperature of 210 degrees F.
Makes 4 large, braided brioche loaves. Refrigerate once cooled if using eggs as they will spoil.