Heat olive oil in a large pot or Dutch oven over medium heat. Add diced onion and sauté for 4-5 minutes until soft and translucent.
Add minced garlic and cook for 1 minute until fragrant, stirring constantly to prevent burning.
Reserve about 1/4 cup of the chopped roasted red peppers for garnish. Add the remaining peppers to the pot along with the diced tomatoes, smoked paprika, and dried oregano. Stir well and cook for 2-3 minutes.
Add the dry pasta and vegetable broth to the pot. Stir to combine, making sure the pasta is submerged.
Bring to a boil, then reduce heat to medium-low. Cover and simmer for 12-14 minutes, stirring every few minutes to prevent sticking, until pasta is al dente and most of the liquid is absorbed.
Stir in the heavy cream, Parmesan cheese, and goat cheese. Mix until the cheeses are melted and the sauce is creamy.
Add the fresh spinach or arugula and stir until just wilted, about 1 minute. Season with salt and pepper to taste.
Serve immediately, topped with reserved roasted red peppers and fresh basil leaves.