Pour warm milk into the bowl of a stand mixer. Stir in the yeast and a pinch of granulated sugar. Let stand for 5 to 10 minutes, or until it has become bubbly.
Add 2 cups of flour to the mixture and stir with a wooden spoon until a smooth batter forms. Cover with plastic wrap and set in a warm spot for 30 minutes. The mixture should have risen and been very bubbly.
In a medium bowl, whisk the egg and egg yolks until pale yellow and frothy, about 3 minutes. Add the sugar, vanilla extract, and salt, and whisk until combined and smooth.
Attach the dough hook to the mixer, add the egg mixture to the dough, and mix on medium-low speed until mostly combined. Add the melted butter and mix to combine. Gradually add 3 more cups of flour to the mixture and continue to knead until a very soft dough comes together. (It will not clean the sides of the bowl or form a ball; it will be rather slack and a bit sticky.) If necessary, add up to another 1 cup of flour, a spoonful at a time, until the dough forms.
Transfer the dough to a lightly greased bowl, cover with plastic wrap, and set in a warm spot until it has doubled in size.
Remove the dough from the bowl and turn it out onto a floured work surface. With your fingers, push down the dough into an even layer. Sprinkle flour on the dough and roll it out to ½-inch thickness. If the dough doesn’t hold its shape and springs back, cover it with a damp towel and let it rest for a few minutes and try again.
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