Heat milk for about 45 seconds in a microwave safe bowl until it is between 90℉ and 120℉.
In a bowl, combine the warm milk, sugar, yeast, vanilla, salt, and 1 cup of the flour. Beat using the paddle attachment until smooth and combined.
1/2 cup (113g) milk, 1/4 cup granulated sugar, 2 teaspoon (6g) instant yeast, 1 1/4 teaspoons (9g) salt, 2 teaspoons vanilla extract
Add the eggs one at a time and mix well after each addition. Add remaining flour, about 1 cup at a time.
4 large eggs, 3 3/4 cups (529g) all-purpose flour
Once all of the flour has been added, start adding the butter about 2 tablespoons at a time while mixing on medium speed. Mix between each addition until the butter is incorporated before adding the next chunk of butter. Once all of the butter has been added, beat for 6-8 minutes. The dough should be very soft and sticky but clear the bottom and sides of the bowl. Stop to scrape the bowl once or twice while mixing.
1/2 cup (113g) salted butter
Transfer the dough to a lightly oiled boil, then cover with plastic wrap and let rise at room temperature for 1 1/2 to 2 hours or until doubled in size. Keep in mind that enriched doughs are heavier and take longer to rise, especially if the room temperature is cooler. If your house is around 68℉ or cooler it can take up to 3 hours to double in size. At this point, you can transfer the dough to the fridge to chill overnight, if desired.
SHAPING OPTION 1 (Braided Loaf): Once the dough has doubled in size, divide it into 6 equal portions and shape into ropes that are about 6-8 inches longer than your bread pan. Braid three of the strands together, then pinch the ends together and tuck the ends under before placing in a 8.5x4.5-inch buttered loaf pan. Cover and let rise until the dough reaches the rim, filling the pan.
SHAPING OPTION 2 (Double-hump Loaf): Once the dough has doubled in size, divide it into 4 equal portions and shape into balls. Place two balls of dough side-by-side into each 8.5x4.5-inch buttered loaf pan. Cover and let rise until the dough reaches the rim, filling the pan and creating a 2-humped brioche loaf with a seam in the middle.
Loosely cover with plastic wrap and let rise again for another 1 1/2 to 2 hours or until puffy and above the rim of the loaf pans. If you chilled the dough in the fridge overnight, this second rise is likely to take more like 3 hours.
During the last 30 minutes of the rising time, preheat the oven to 350℉ (177℃). Before baking, beat an egg in a small bowl and gently brush it on the top of the loaves with a pastry brush. Sprinkle with Swedish sugar pearls, if desired for a sweet brioche loaf. Bake for 30 to 35 minutes or until golden brown on top and an instant digital thermometer reads 190℉ when you test the bread. The bread will also sound hollow when thumped.
egg wash
Remove the loaves from the pans immediately after removing them from the oven and let them cool on a wire cooling rack for 1 hour before slicing and serving.