Focaccia with Caramelized Onions and Spinach

For the Focaccia Dough:

all-purpose flour, plus more as needed

bread flour

instant dry yeast

salt

lukewarm water (100 to 110 degrees F)

good-quality olive oil, plus more for oiling

cornmeal for dusting

For the Topping:

good-quality olive oil, divided, plus more for brushing

medium red onion, thinly sliced

loosely packed baby spinach

Tb chopped, fresh rosemary

Tb chopped, fresh thyme

salt,

freshly ground black pepper,

dried oregano,

shredded whole-milk mozzarella or other cheese of your choosing

freshly grated Pecorino Romano or other hard cheese or your choosing, plus more for sprinkling

red pepper flakes,