Place all ingredients in the bowl of a stand mixer fixed with a paddle attachment and mix until just combined. Replace paddle attachment with dough hook and knead dough until smooth and elastic, about 7 minutes (or knead by hand on a lightly floured countertop for about 10 minutes).
Form dough into a ball, place in a lightly greased bowl, cover, and let rise until doubled, about 1 1/2 to 2 hours.
Preheat oven to 450 degrees F. Remove risen dough from bowl and punch down. Divide in half and shape each piece into a 10-12 inch round or 8-by-12 inch rectangle. Place rounds or rectangles onto pizza stones or parchment paper-lined baking sheets.
For thin crust, bake pizza immediately. For medium to thick crust, let dough rest for about 30 minutes.
Bake crusts without anything on them for about 5 minutes. Add meat and veggie ingredients and bake another 10 minutes. Add half the cheese and any herbs and bake another 3 minutes, then add remaining cheese and bake until cheese is just melted, about 3 more minutes.
Remove from oven and let rest 10 minutes before slicing.