In a glass bowl or large measuring cup, combine milk, 1/4 cup sugar, and yeast. Leave this mixture in a warm place for about 20 minutes. Once it becomes frothy, give it a quick stir.
Mix all ingredients (but butter) in a stand mixer
Place the flour (start with 7 cups) and salt, and 3/4 cup sugar in the bowl of a stand mixer. Then pour the warm yeast mixture into the bowl.
Crack the eggs into a bowl and give them a quick whisk just to loosen them. Add the beaten eggs and vanilla extract to the rest of the ingredients in the mixer bowl.
Using the hook attachment, beat the dough until it begins to come together.
Knead in the softened butter
Cut the butter into slices and add 1/2 cup. Continue kneading the dough until the butter is well incorporated.
Add the remaining 1/2 cup sliced butter and knead the dough on high speed for about 10 minutes or until the dough is smooth and elastic. If the dough isn't coming together well enough, add the remaining 1/4 cup flour.
Rise the dough in a greased bowl
Place the dough onto a lightly floured surface and round it into a ball. Place it into a bowl greased with oil (lightly grease the top of the dough as well). Then cover with a cheesecloth and leave in a warm place for 1 hour or until it doubles in size.
Braid the dough and rise again
Once the dough has proofed, divide it into two equal pieces. These two halves will make two loaves of bread.
Starting with one of the two dough halves, divide that half into three equal balls. Roll those three balls into long strands.
Begin crossing over the three strands in a braid-like fashion. Once you get the end, pinch the dough to seal the braid. Repeat steps 8-9 with the other dough halve. (If you don't want to do a braid, just place the 3 dough balls on the loaf pan.)
Brush with egg wash and bake
Spray a loaf pan with nonstick spray and place the braided dough into the pan. Cover with a cheesecloth and let it proof in a warm place for 1 hour or until it doubles in size.
Once the dough has proofed, brush with egg wash (1 beaten egg + 1 tsp water). Bake at 350 degrees Fahrenheit for 40 minutes until golden brown.
TIPS:The dough should be sticky (because of all the butter and eggs). This will give it that fluffy texture. if the dough is too runny, add 1/4 cup flour at a time, and mix well. How to store it: Keep the brioche in a plastic bag at room temperature for up to 4-5 days. The more airtight the bag, the fresher the bread will taste.