Sheet-Pan Pepperoni Pasta

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1. 1
   Preheat oven to 400°. Whisk together 3 garlic cloves, finely grated, one 4.5-oz. tube double-concentrated tomato paste (about ½ cup), ⅓ cup extra-virgin olive oil, 1 Tbsp. dried oregano, 1½ tsp. Diamond Crystal or 1 tsp. Morton kosher salt, 1 tsp. freshly ground black pepper, and ¼ tsp. crushed red pepper flakes (if using) in a medium bowl. Add 1 medium red or yellow onion, thinly sliced, and one 8–10-oz. package button mushrooms, thinly sliced, and mix to coat vegetables. Spread out onto a large rimmed baking sheet. Bake, tossing halfway through, until vegetables have shrunk and tomato paste is darkened and starting to stick to baking sheet, 25–30 minutes. Remove from oven and increase oven temperature to 450°.
2. 2
   Meanwhile, cook 1 lb. rigatoni or other short pasta in a large pot of boiling salted water until very al dente, about 2 minutes less than package directions. Drain, reserving 2½ cups pasta cooking liquid. Return pasta to pot.
3. 3
   Drizzle 1 cup pasta cooking liquid over vegetables on baking sheet and scrape vegetable mixture into pot with pasta. Toss, gradually adding 1½ cups pasta cooking liquid, until combined; season with more salt and black pepper. Return pasta mixture to baking sheet and spread out.
4. 4
   Scatter 6 oz. low-moisture mozzarella, coarsely grated (about 1 cup), and 2 oz. Parmesan, finely grated (about 1 cup) over pasta. Dot surface with 3 oz. pepperoni, thinly sliced. Bake until cheese is melted and starting to brown in spots and pepperoni is crisp, 12–15 minutes.
5. 5
   Remove pasta from oven and top with sliced banana peppers from a jar, sliced black or green olives, and/or oil-packed anchovy fillets as desired. Sprinkle with more oregano and crushed red pepper flakes (if using).