Boil the pasta: Bring a large pot of salted water to a rolling boil. Add the pasta and cook until al dente according to package directions. Reserve 1/2 cup of the starchy cooking water, then drain.
Season the chicken: Pat the chicken dry.
Toss with 1/2 teaspoon salt, black pepper, and garlic powder. Dry surfaces sear better, giving you more flavor.
Sear the chicken: Heat the olive oil in a large skillet over medium-high heat. Add the chicken in an even layer.
Cook, without moving, for 2–3 minutes to brown, then stir and cook another 3–4 minutes until cooked through. If the pan looks dry, add a splash more oil.
Lower the heat: Reduce to low. Add the drained pasta to the skillet with the chicken.
Add pesto and cheese: Stir in the pesto and Parmesan.
Splash in some of the reserved pasta water to loosen the sauce. You want it silky, not gloopy—start with a few tablespoons and add as needed.
Finish and brighten: Fold in cherry tomatoes and greens, if using, until just wilted. Squeeze in the lemon juice.
Taste and adjust with the remaining 1/2 teaspoon salt if needed. Add red pepper flakes for gentle heat.
Serve: Plate hot with extra Parmesan on top. If the pasta sits and thickens, loosen with a spoonful of hot water or a drizzle of olive oil.