Bring a large pot of well-salted water to a rolling boil. Add the pasta and cook until just shy of al dente, according to package directions. Drain and rinse the pasta with cool water. Set aside to cool entirely before assembling.

In a high-speed blender or in a food processor, add the roasted red peppers, shallot, garlic, tomato paste, lemon zest and juice, red wine vinegar, olive oil, almonds, paprika, oregano, salt, pepper, and red pepper flakes (if using). Blend on medium speed until totally smooth, 1 to 2 minutes. Set aside.

In a medium skillet set over medium heat, add the diced chorizo and cook until the fat is rendered and the edges are browned and crispy, 5 to 7 minutes. Use a slotted spoon to transfer the sausage to a paper towel-lined plate. Keep the reserved grease in the pan. You should have about 1 tablespoon.

To the remaining grease, add the breadcrumbs, oregano, salt, and pepper and stir to combine. Cook, stirring often, until deeply golden and toasty, about 4 minutes. Set aside to cool.

Add the cooled pasta and romesco sauce to a large mixing bowl and toss to combine. Add the grape tomatoes, olives, manchego cheese, crispy chorizo, parsley, and about 1/2 of the breadcrumb mixture and toss to combine. Taste and season with more salt, if needed.

Garnish with the remaining breadcrumbs and more parsley. Serve cold or room temperature.