Heat olive oil in a large skillet, over medium heat. Add pancetta; cook, stirring, until lightly browned, 6–8 minutes. Add cracked black pepper; cook until fragrant, about 2 minutes more.
Increase the heat to medium-high; add garlic, carrots, and onions and cook, stirring occasionally, until soft, about 6 minutes. Add chili flakes; cook for 1 minute.
Stir in tomatoes, breaking them into bite size pieces with a wooden spoon. Reduce the heat to medium-low, and simmer with lid on, stirring occasionally, until sauce thickens, about 20–25 minutes. Season with salt; keep warm.
While sauce cooks, bring a large pot of water to a boil. Add 1 tablespoon salt to the pasta water. Add pasta and cook until just al dente, 6–8 minutes.
Reserve ½ cup pasta water from the pot then drain pasta. Heat reserved sauce over medium heat. Add pasta and reserved water; cook, tossing, until sauce clings to pasta, 2–3 minutes. Add ½ cup Pecorino; toss. Divide between serving bowls; serve with remaining Pecorino. Top with chiffonade threads of basil if desired.