Preheat oven to 450° F.
Drizzle a rimmed sheet tray with 2 tablespoons olive oil and evenly spread to coat the surface.
Add pizza dough to baking pan and turn to coat. Gently pat and stretch dough into the four corners of the pan to make a rectangle-like shape.
Spread sauce evenly over the dough leaving a 1/2-inch crust. Sprinkle evenly with the mozzarella.
Add Brussels sprouts, shallots and rosemary.
Drizzle with remaining 1-tablespoon olive oil and season with salt and pepper. Top with Parmesan cheese.
Bake for 20 to 25 minutes.
Garnish with chives. Top with shaved Parmesan. Slice into squares for serving.