Bring a large pot of salted water to a boil. Once boiling, add pasta and cook until al dente. Before draining, reserve 1 cup of pasta cooking water.
While the pasta boils, heat oil in a large skillet over medium-high. Once hot, add onions; cook 7 to 8 minutes, or until soft. Add garlic, tomato paste, smoked paprika, and chili flakes. Cook 3 to 5 minutes, stirring occasionally, until the tomato paste turns brick red.
Add sherry and broth, and stir to release any browned bits stuck to the bottom of the pan. Simmer 3 to 4 minutes, until the liquid slightly reduces. Stir in salt and black pepper.
Transfer mixture to a high power blender, and add roasted red peppers. Blend until smooth, about 30 to 45 seconds. Transfer sauce back to the pan, and stir in heavy cream.
Combine pasta, spinach, and red pepper sauce in pan over medium-low heat (if pan is too small, combine all ingredients in the pot you boiled pasta in). Stir continuously until spinach wilts down and sauce begins clinging to noodles. Stir in reserved pasta cooking water in 1/4 cup increments until desired consistency is achieved. (I always end up using the full 1 cup.) Add basil and sprinkle in Parmesan cheese, stirring continuously, until combined.
Garnish with extra Parmesan and basil upon serving, if desired.