Bring a large pot of salted water to a rolling boil. Cook the pasta 1 to 2 minutes less than package directions so it finishes in the sauce; before draining, scoop out and save 1 cup of the starchy pasta water.
While the pasta cooks, warm 1 tablespoon of olive oil in a large skillet over medium heat. Add the chopped onion and a pinch of salt and sauté until translucent and softened, about 4–5 minutes. Add the garlic and cook another 30 seconds until fragrant.
Add the drained roasted red peppers, the remaining 1 tablespoon oil, vegetable broth, heavy cream, smoked paprika, and black pepper to the pan. Bring the mixture to a low simmer for 1–2 minutes to warm through.
Transfer the pepper-cream mixture to a blender (or use an immersion blender directly in the pan) and puree until completely smooth and silky. Return the sauce to the skillet and simmer gently, uncovered, 6–8 minutes to reduce and thicken slightly.
Off the heat, stir in the grated Parmesan until melted. If the sauce feels too thick, whisk in 2–4 tablespoons of the reserved pasta water until you reach a glossy, clingy consistency.
Add the drained pasta to the sauce and toss over low heat for about 1 minute so the pasta absorbs the flavor. Let the pan sit off heat for 2 minutes to let the sauce set and thicken slightly.
Divide among bowls and finish with an extra sprinkle of Parmesan and a crack of black pepper. Serve immediately.