In the bowl of a stand mixer with the dough hook attachment, mix together the flour, sugar, salt, and yeast.
With the mixer on low, slowly add butter, milk, water, vanilla, and then eggs. Turn the mixer on medium-low and knead until the dough is soft and smooth (about 2 minutes). If it seems too dry add a little water, if it seems too sticky add just a little flour, up to a 1/4 cup.
Place the dough in a lightly greased bowl, cover, and allow to rest until doubled in size, about 1 hour.
Gently deflate the dough and turn it out onto a lightly floured surface.
Roll the dough into a 12" x 20" rectangle.