Season the chicken: Pat dry. Rub with 2 tbsp olive oil, 1 tsp salt, 1/2 tsp pepper, and garlic powder.
Let sit while you heat the grill pan or outdoor grill.
Grill the chicken: Cook over medium-high heat 5–6 minutes per side, until the thickest part hits 165°F. Rest on a board for 5 minutes, then slice.
Cook the spaghetti: Boil in well-salted water until just shy of al dente. Reserve 3/4 cup pasta water, then drain.
Start the sauce: In a large skillet, melt butter over medium heat.
Add minced garlic and cook 30 seconds until fragrant, not browned.
Add cream: Pour in the heavy cream and bring to a gentle simmer. Cook 2–3 minutes to slightly thicken.
Stir in cheese: Reduce heat to low. Whisk in Parmesan until smooth.
Add 1/2 cup pasta water to loosen and emulsify.
Pesto and lemon: Stir in pesto, lemon zest, and lemon juice. Taste and adjust salt and pepper. Add a pinch of red pepper flakes if you like heat.
Toss the pasta: Add drained spaghetti to the skillet and toss until coated.
If it seems tight, splash in more pasta water a little at a time until silky.
Finish with chicken: Fold in sliced grilled chicken. Warm through for 1 minute. Serve topped with extra Parmesan and torn basil.