To make the romesco sauce, add the sun-dried tomatoes, roasted red bell peppers, walnuts, olive oil, parmesan, lemon juice, garlic, smoked paprika, salt, black pepper, and red pepper flakes to a food processor or blender. Blend until smooth and creamy. Taste and adjust the seasoning if needed, then set aside.
Bring a large pot of salted water to a boil and cook the pasta according to package directions. Reserve a little pasta water, then drain and set aside.
In a large skillet over medium heat, melt the butter with the olive oil. Add the garlic and sauté for about 1 minute until fragrant and golden.
Add the romesco sauce and stir to warm it through. Pour in the heavy cream and mix until smooth. Season with red pepper flakes, salt, and black pepper to taste.
Toss the cooked pasta into the sauce and mix well until every piece is coated. Add in the parmesan and stir until it melts into the sauce. If the sauce is too thick, add a splash of the reserved pasta water to loosen it up. Feel free to add more cheese at this step.
Serve warm with extra parmesan on top and a sprinkle of red pepper flakes if you want a kick or chopped walnuts if you want a crunch.