Place a rack directly underneath broiler in oven; preheat to 450°F. Make sure bottom of oven is accessible (that’s right, you’re going to bake directly on the bottom of your oven).
Start by trimming Brussels sprouts. Slice each sprout in half lengthwise.
Set aside about 1/4 of the halves, then transfer remaining sprouts to a rimmed baking sheet. Add garlic, and drizzle with oil; season with salt and red pepper flakes. Toss to combine and arrange sprouts cut sides down.
Place baking sheet on floor of oven (NOT on a rack) and roast, turning sprouts halfway through with a spatula, until sprouts are deeply browned on all over and tender all the way through, 15–18 minutes. Let cool.
While Brussels are roasting and cooling, prep your other ingredients. Remove casing from 3 oz. salami and slice into thin rings, then cut rings into quarters. Slice 12 oz. mozzarella into planks that are no more than ¼" thick. Peel 1 shallot and cut crosswise into thin rings. Place shallot rings in a small bowl. Cut lemon in half and squeeze halves into bowl. Add a pinch of salt and toss; set aside.
When Brussels are cool enough to handle, scrape into a medium bowl and set aside. Reserve sheet tray. Fish out garlic and squeeze cloves from skins. Mash garlic to a paste in another small bowl with a fork. Add 2 Tbsp. oil and stir to combine.
Place dough in center of reserved baking sheet and drizzle with 1 Tbsp. oil, then toss to coat. Use your fingers to stretch dough outward from center all the way to edges of baking sheet. If dough stubbornly springs back, cover with plastic wrap and let rest a few minutes before attempting to stretch again.
Drizzle garlic-oil over dough and spread around with your fingers to coat. Season with salt, then top with mozzarella, roasted Brussels, and salami, distributing evenly. (Reserve bowl that held Brussels.)
Bake pizza on floor of oven until underside is browned and edges are puffed and starting to turn golden, 7–10 minutes (lift up edge of pizza with spatula to peek underneath).
While pizza is baking, thinly slice remaining Brussels sprouts crosswise and add to bowl that had the roasted sprouts. Toss with remaining 1 Tbsp. oil and season with salt.
Remove pizza from oven and turn broiler to high. Scatter sliced Brussels over pizza.
Broil pizza on top rack until cheese is bubbling and browned and edges of crust are deep golden, 2–3 minutes.
Top with more red pepper flakes. Drain shallot and scatter rings over pizza.