Bring a large pot of salted water to a rolling boil. Add 12 oz strozzapreti and cook until just shy of al dente according to package instructions (usually 9–11 minutes). Reserve 1 to 1 1/4 cups of the pasta cooking water, then drain the pasta and set aside.

Season shrimp

While the pasta cooks, pat 1 lb shrimp dry and season with 1 tsp kosher salt and 1 tsp freshly ground black pepper.

Cook shrimp with Calabrian chili

Heat 2 tbsp extra-virgin olive oil in a large skillet over medium-high heat until shimmering. Add the seasoned shrimp in a single layer and sear 1–1.5 minutes per side until pink and just cooked through. Push shrimp to one side of the pan. Add 2 tbsp Calabrian chili paste to the hot oil; stir briefly to bloom the chile flavor (about 20–30 seconds). Deglaze with 1 tbsp white wine (or stock), scraping any brown bits from the pan. Toss shrimp with the chile sauce; remove from heat and keep warm.

Pesto

Assemble pesto

In a food processor, combine 2 cups packed fresh basil, 1 cup roasted red peppers (drained), 1 cup cooked gigante beans, 1 cup grated Parmigiano-Reggiano, 1 tbsp toasted pine nuts, 1 large garlic clove, and 1 tbsp fresh lemon juice. Pulse until coarsely combined.

Emulsify

With the processor running, slowly stream in 1 cup extra-virgin olive oil until a creamy, slightly textured pesto forms. Stop and scrape down the bowl as needed. Taste and adjust seasoning with 1 tsp salt and 1/2 tsp black pepper. If the pesto is too thick, thin with 2–4 tbsp reserved pasta water to reach a saucy consistency.

Greens & Finish

Combine pasta and pesto

Return the drained pasta to the large pot or a warmed skillet over low heat. Add 1/2–3/4 cup of the pesto (reserve some for serving) and 1/2 cup of reserved pasta water. Toss vigorously until the pasta is evenly coated, adding more pasta water as needed to loosen the sauce and create a glossy emulsion.

Fold in shrimp and greens

Add the Calabrian chili shrimp to the pesto-coated pasta along with 2 cups baby arugula. Toss briefly off the heat until the arugula wilts slightly and everything is combined.

Plate and garnish

Divide the pasta among 4 plates. Spoon any remaining pesto over the top as desired. Drizzle each portion with 1 tbsp finishing olive oil, sprinkle 1/2 tsp lemon zest across the batch (optional), and garnish with fresh basil leaves. Taste and adjust with additional salt, pepper, or Calabrian paste to taste.