Butterfly the chicken breast, season with salt and pepper, and sear 2–3 minutes per side in olive oil. Remove and rest.
Add pasta to a skillet with ~4 cups water and a pinch of salt. Boil 8–10 minutes until just shy of al dente. Reserve 1 cup pasta water.
In the same pan, sauté garlic, shallot, and tomatoes until softened. Deglaze with lemon juice or a splash of water.
Stir in Calabrian chili paste 1 spoonful at a time. Add lemon or orange to balance heat and brighten flavor.
Lower heat. Add Pecorino, a splash of pasta water, and butter or olive oil to create a glossy, smooth sauce.
Add pasta and reserved chicken back to the pan. Toss until coated. Adjust thickness with pasta water.
Top with herbs, black pepper, and extra cheese. Serve hot—or let cool for cold pasta salad.
