Pat the chicken breasts dry and season generously with salt and pepper. Heat olive oil in a large skillet over medium-high heat until shimmering, and then carefully add the chicken breasts.
Sear the chicken without moving for about 4-5 minutes until the bottoms are golden brown and release easily from the pan. Flip and cook another 4-5 minutes until the second side is golden and the chicken is cooked through. Remove to a plate and set aside.
Lower the heat to medium, add the minced garlic to the same pan, and sauté for about 30 seconds until fragrant and slightly golden, stirring constantly to avoid burning.
Add the chopped sun-dried tomatoes to the skillet and cook for 2 minutes, stirring often, to release their smoky aroma and soften slightly.
Pour in the heavy cream and sprinkle in the grated Parmesan cheese, stirring constantly as the sauce begins to thicken and become silky, about 3-4 minutes.
Return the chicken breasts to the skillet, nestling them into the sauce. Cover and let simmer on low heat for 8-10 minutes, until the chicken is cooked through and tender.
Uncover and add the fresh spinach, stirring until wilted and vibrant green, about 1-2 minutes. The sauce should be glossy and coats the chicken evenly.
Transfer the chicken to serving plates, spoon the sauce over the top, and garnish with extra Parmesan or herbs if desired. Let rest for 2 minutes before slicing and serving hot.