Set a large skillet over medium-high heat and warm 2 tablespoons of the olive oil. Sprinkle salt and pepper over both sides of each chicken breast.
Place the chicken in the hot oil and cook for about 5–7 minutes on each side, until golden brown and cooked through. Transfer the breasts to a plate.
Pour the remaining 1 tablespoon of olive oil into the same skillet. Stir in the finely chopped garlic, thyme leaves, and crushed red pepper flakes, and sauté for about 1 minute, just until fragrant.
Add the chicken broth, scraping the skillet bottom to release the browned bits. Simmer for 2–3 minutes.
Stir the sun-dried tomatoes, heavy cream, and Parmesan into the broth. Keep at a simmer for 3–4 minutes, allowing the sauce to thicken a little.
Place the cooked chicken back in the skillet and spoon sauce over the breasts. Simmer everything together for another 2–3 minutes, until the chicken is heated through.
Scatter torn fresh basil over the chicken. Serve with the sauce over pasta or rice, or pair it with crusty bread.
Notes
Offer the chicken and sauce over pasta or rice, or serve with crusty bread.