Fill a large pot with water, place it over high heat, and bring it to a boil.

Set a large skillet over medium heat. Add the chopped walnuts and toast them for 2 to 3 minutes, stirring often, until they smell nutty and look a shade darker.

Transfer the toasted walnuts to a small bowl. Set 2 tablespoons aside for serving.

When the pot of water reaches a full boil, add 2 teaspoons of the kosher salt.

Add the rigatoni to the boiling water and stir right away so the pieces do not stick together. Cook according to the package until the pasta is tender but still has a little firmness in the center, usually 10 to 12 minutes.

While the pasta cooks, return the skillet to medium heat and add the olive oil.

Add the chopped onion to the skillet. Cook for 5 to 6 minutes, stirring now and then, until the onion is soft and lightly golden at the edges.

Add the sliced garlic and 1/2 teaspoon of the black pepper to the skillet. Cook for 30 seconds, stirring, just until the garlic smells fragrant.

Put the drained roasted red peppers into the skillet. Cook for 2 minutes, stirring, until the peppers are hot and glossy.

When the pasta is almost ready, scoop 1 cup of the pasta cooking water into a heatproof measuring cup and set it near the stove.

Transfer the onion and pepper mixture from the skillet to a blender. Add the toasted walnuts from the bowl, except for the 2 tablespoons you reserved for serving.

Add 1/2 cup of the reserved pasta water and 1/2 cup of the grated Parmesan to the blender. Blend until the sauce is very smooth and orange-red, about 30 to 45 seconds.