Cook the pasta: Bring a large pot of salted water to a boil. Cook the pasta until just al dente.
Reserve at least 1/2 cup of the cooking water, then drain.
Make the pesto: In a food processor, add basil, parmesan, nuts, garlic, salt, pepper, and lemon juice. Pulse to combine. With the motor running, stream in 1/3 cup olive oil.
Add more oil until the texture is silky but still thick. Taste and adjust salt or lemon.
Season the chicken: Pat chicken dry. Toss with salt, pepper, garlic powder, and crushed red pepper if using.
Cook the chicken: Heat 1 tablespoon olive oil in a large skillet over medium-high.
Add chicken in a single layer. Sear without moving for 2–3 minutes, then stir and cook 3–4 more minutes until cooked through and lightly browned. Transfer to a plate.
Quick tomato toss (optional): In the same pan, add the cherry tomatoes and a pinch of salt.
Cook 1–2 minutes just until they soften and release some juice. Turn off the heat.
Combine: Add drained pasta and chicken to the skillet. Spoon in the pesto and a splash (2–4 tablespoons) of pasta water.
Toss until the sauce coats the pasta. Add more water as needed to loosen. Keep the heat low to avoid dulling the basil flavor.
Finish and serve: Taste and add salt, pepper, or a squeeze of lemon.
Top with extra parmesan and torn basil. Serve warm.