Prep the chicken: Pat chicken dry.
Slice thick breasts horizontally to make thinner cutlets for quicker, even cooking. Season both sides with salt, pepper, and a light sprinkle of garlic powder.
Brown the chicken: Heat olive oil and butter in a large skillet over medium-high heat. Sear chicken 3–4 minutes per side until golden.
Remove to a plate; it will finish cooking in the sauce.
Deglaze and build flavor: Lower heat to medium. Pour in chicken broth and scrape up browned bits with a wooden spoon. Reduce by about half, 2–3 minutes.
Add cream and pesto: Stir in heavy cream and pesto.
Simmer gently for 2–3 minutes until slightly thickened. Taste and adjust salt and pepper.
Finish the chicken: Return chicken (and any juices) to the pan. Simmer 4–6 minutes, spooning sauce over, until chicken is cooked through (internal temp 165°F/74°C).
If sauce is too thick, splash in a bit more broth or cream.
Stir in extras: Fold in Parmesan and spinach until wilted, 30–60 seconds. Add cherry tomatoes for brightness, if using. Finish with lemon zest, a squeeze of lemon juice, and a pinch of red pepper flakes.
Serve: Spoon plenty of sauce over each piece.
Garnish with fresh basil and extra Parmesan. Pair with sautéed zucchini, roasted broccoli, or mashed cauliflower.