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Stir together warm milk and 2 teaspoons sugar in
bowl of mixer. Sprinkle yeast over mixture and let
stand until foamy, about 5 minutes. (If yeast
doesn't foam, discard and start over with new
yeast.)
Add 1/2 cup flour to yeast mixture and beat at
medium speed until combined. Add whole eggs, yolk,
vanilla, salt, and remaining 1/2 cup sugar and
beat until combined. Reduce speed to low, then mix
in remaining 2 3/4 cups flour, about 1/2 cup at a
time. Increase speed to medium, then beat in
butter, a few pieces at a time, and continue to
beat until dough is shiny and forms strands from
paddle to bowl, about 4 minutes. (Dough will be
very soft and sticky.)
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