Prepare no-knead pizza dough as directed, leaving dough in one large ball instead of dividing into four pieces.
Heat oven to 425F; place an oven rack on the lowest position in the oven. In a large non-stick skillet over medium heat, cook and crumble Italian sausage 8-10 minutes until cooked through. Drain, reserving 1 tablespoon drippings. Return drippings to skillet and heat over medium heat. Add shredded Brussels sprouts to skillet. Stir and cook 5-6 minutes until sprouts are tender and just beginning to brown.
Spray bottom and sides of a 9x13-inch pan with cooking spray. Press room-temperature pizza dough into bottom and sides of pan (if dough resists, let it rest for 10 minutes, then press out again). Spread 1/3 cup pesto evenly over dough to within 1/2-inch of edges. Top with 1 cup mozzarella cheese, then top with approximately half of cooked Italian sausage and half of cooked Brussels sprouts. Top with another 1/2 cup mozzarella cheese.
Bake 25-30 minutes until dough is baked through and cheese is fully melted and beginning to brown. Immediately top baked pizza with remaining 1/2 cup mozzarella cheese, 3 tablespoons pesto, and remaining half of Italian sausage and Brussels sprouts. Sprinkle with Parmesan cheese.
Let pizza rest 5 minutes before cutting into squares.
Notes
I shredded my Brussels sprouts with a box grater, but you can also buy them pre-shredded at the grocery store. Either way works here.