Pat chicken dry with paper towels, then season both sides with salt and black pepper.

Heat olive oil and 1 tbsp butter in a large skillet over medium-high heat. Cook chicken 5–6 minutes per side until golden and internal temp reaches 165 °F. Transfer to a plate to rest.

Reduce heat to medium, melt remaining 2 tbsp butter, and sauté garlic for about 30 seconds until fragrant.

Pour in chicken broth, scraping up browned bits. Stir in cream and simmer 3–4 minutes. Gradually whisk in Parmesan until smooth, about 2 minutes. Season with salt and pepper.

Meanwhile, cook pasta in salted boiling water until al dente, 8–10 minutes. Reserve 1 cup pasta water, then drain.

Slice chicken and return to skillet. Add pasta and toss in the sauce, adding reserved water as needed for creaminess.

Sprinkle with parsley and serve hot with extra Parmesan.