Arrange bread slices on a sheet pan and tuck walnuts into the empty spots. Slide the pan into a 350°F oven and toast for 8 to 10 minutes, tossing the walnuts and flipping the bread halfway so the nuts brown lightly and the bread shows a bit of golden color.
Tear the toasted bread into small pieces and add them to a food processor. Pulse repeatedly until you have coarse crumbs with little bits of texture, keeping the processor off continuously to avoid a fine powder.
Add half your toasted crumbs to the processor along with roasted red peppers, walnuts, garlic, lemon juice, smoked paprika, red pepper flakes, salt, and pepper. Process until a thick paste forms, scrape down the sides, then stream in olive oil until the sauce is smooth and thick. Taste and adjust seasoning.
Transfer room temperature pasta to a large bowl and pour the red pepper sauce over it. Use a silicone spatula to move the pasta gently and spread the sauce evenly.
Add about ¾ cup of reserved pasta water and toss so the sauce loosens and clings to each piece. If the mixture feels too thick, add a little more water until it looks saucy.
Fold in chopped arugula and any other mix-ins you like—diced roasted peppers or seasonal tomatoes work well—and toss until the greens soften slightly and the flavors meld.
Before serving, sprinkle the reserved herby bread crumb topping over the salad and toss gently so you get bursts of fresh herbs and crunchy crumbs in every bite.