Heat oil in a large pot or Dutch oven over medium; sauté onion 4-5 minutes until soft and translucent.
Cook garlic 1 minute until fragrant, stirring constantly to prevent burning.
Reserve about 1/4 cup peppers for garnish; add remaining peppers, tomatoes, paprika, and oregano, stir, and cook 2-3 minutes.
Stir in dry pasta and broth, keeping pasta submerged.
Boil; reduce heat to medium-low, cover, and simmer 12-14 minutes, stirring every few minutes to prevent sticking, until pasta is al dente and most liquid absorbed.
Stir in cream, Parmesan, and goat cheese until melted and creamy.
Add spinach or arugula; stir about 1 minute until just wilted and season with salt and pepper.
Serve immediately, topped with reserved roasted red peppers and fresh basil leaves.