Season the Chicken : Pat the chicken breasts dry with a paper towel. In a small bowl, combine the smoked paprika, red pepper flakes (if using), and half of the salt and pepper (¼ tsp salt, ⅛ tsp pepper). Sprinkle the seasoning mixture evenly over all sides of the chicken.
Develop the Sear : Place the sauté pan over medium-high heat and add the sun-dried tomato oil. Once the oil shimmers, carefully place the seasoned chicken in the pan in a single layer. Cook for 3-4 minutes per side, until a deep golden-brown crust forms. The chicken will not be cooked through at this stage.
Sauté the Aromatics : Push the seared chicken to one side of the pan. Add the diced yellow onion to the empty side and cook for about 2 minutes, stirring frequently, until it begins to soften. Add the minced garlic and cook for another 45 seconds until fragrant.
Deglaze and Build the Base : Pour the white wine into the pan to deglaze, using a wooden spoon to scrape any browned bits from the bottom. Allow the wine to bubble and reduce by about half, which should take about 1 minute.
Create the Cream Sauce : Reduce the heat to medium-low. Stir in the chicken broth, heavy cream, julienned sun-dried tomatoes, and the remaining salt and pepper. Bring the liquid to a gentle, steady bubble.
Simmer to Perfection : Arrange the chicken breasts within the sauce. Allow the dish to cook, uncovered, for 8-10 minutes. The sauce will thicken slightly and the chicken will finish cooking. Confirm doneness when an instant-read thermometer inserted into the thickest part of the chicken registers 165°F (74°C).
Finish and Garnish : Turn off the heat. Stir the grated Parmesan cheese into the sauce until it melts smoothly. Sprinkle the fresh basil over the top and serve immediately, spooning extra sauce over each piece of chicken.
