Boil the pasta: Bring a large pot of salted water to a boil.
Cook the pasta until just shy of al dente. Before draining, reserve 3/4 cup of pasta water.
Toast the nuts: In a dry skillet over medium heat, toast the nuts for 3–4 minutes until fragrant. Let them cool slightly.
This step boosts flavor and helps the pesto turn silky.
Make the pesto base: In a food processor, add the roasted red peppers, basil, toasted nuts, garlic, lemon zest, and lemon juice. Pulse until mostly smooth.
Add cheese and spice: Add Parmesan (if using) and crushed red pepper flakes. Season with a pinch of salt and black pepper.
Pulse a few times to combine.
Stream in olive oil: With the motor running, slowly stream in 1/3–1/2 cup olive oil until the sauce looks creamy and cohesive. Taste and adjust salt, pepper, and lemon.
Combine with pasta: Return the drained pasta to the warm pot. Add the roasted red pepper pesto and 1/2 cup of reserved pasta water.
Toss over low heat for 1–2 minutes until the sauce clings to the noodles. Add more pasta water as needed for a glossy finish.
Adjust and serve: Stir in a spoonful of ricotta or mascarpone if you want a richer sauce. Finish with extra Parmesan, a drizzle of olive oil, and a crack of black pepper.
Serve hot.