Cook cavatelli pasta according to the directions on the package. Reserve ½ a cup of the starchy cooking water and strain.
Heat olive oil on medium in a large pot or skillet. Add sliced chorizo and cook for 7 minutes or until it starts to crisp up, stirring occasionally. Set crispy chorizo aside on a plate, saving the oil that remains in the skillet.
In the same skillet, add the onion and cook for 4 minutes or until it starts to become tender.
Reduce the heat to medium-low and add garlic, roasted red peppers, tomatopaste, paprika and salt. Stir occasionally for 3 minutes or until you can start to smell the smoky paprika.
Add in the reserved pasta water and stir until the sauce just starts to the thicken. Add the pecorino romano and continue to stir until the cheese is melted and the sauce is thick and glossy.
Add the cooked cavatelli to the sauce and toss gently until everything is incorporated. Serve and top with red pepper flakes (if using).