Preheat oven to 450º F.

Prep the sprouts by slicing off the tough bottom ends and discarding them. On half the sprouts, peel off individual leaves, discarding the tough middle. On the other half, shred them as finely as you can, using a knife or mandolin, discarding the tough bottoms. Drizzle the sprouts with 2 teaspoons olive oil and toss well until they're all lightly coated in oil (add another teaspoon of oil if necessary).Toss with a good pinch of salt and pepper and set aside.

Heat 1 tablespoon olive oil in a large skillet over medium heat. Add the onions and a good pinch of salt and toss to combine. Cover and cook, stirring occasionally, for 5 minutes, or until the onions begin to soften. Uncover and cook until translucent and tender, 5 minutes more. Add the garlic and cook for 30 seconds. Pour in the balsamic vinegar and cook while stirring for a few more minutes, until the vinegar has mostly soaked into the onions. Remove from heat and set aside to cool.

Roll out the pizza dough onto a sheet of parchment paper set on a baking tray. Leaving the edge free, spread out an even layer of red onions, then the mozzarella cheese. Add the sprouts on top, mixing up the leaves and shredded pieces. Top with a drizzle of olive oil, if desired and a good sprinkle of freshly cracked black pepper.

Transfer pizza to the oven at a time and bake until the crust is puffy and brown and the sprouts are crispy on the edges, about 12-15 minutes. As soon as the pizza does out, sprinkle on crumbles of goat cheese and more black pepper, if desired.