Cook pasta according to package instructions in a large pot of salted water. During final 5 minutes, add broccoli to pot. Reserve 1 cup pasta water, and drain remaining. Return cooked pasta and broccoli to pot.
Meanwhile, prepare sunflower seed romesco by combining roasted red peppers, sunflower seeds, tomato paste, lemon zest and juice, garlic, smoked paprika, red pepper flakes, and parsley in a high power food processor or blender. Blend on high speed, gradually streaming in olive oil, until smooth. Season to taste with salt and pepper.
Pour romesco sauce into pot with pasta and broccoli; toss to combine. Gradually stream in reserved pasta water in 1/2 cup increments, tossing continuously, until pasta sauce appears glossy (you may not need the full cup). Garnish with Parmesan cheese, nutritional yeast, herbs, or lemon wedges, if desired.