Prepare the chicken: Pat the chicken breasts (4) dry with paper towels. Pound the thicker end of each breast until the entire breast is an even 1/2-inch thick. Season both sides with the salt (3/4 teaspoon), pepper (1/2 teaspoon), garlic powder (1 teaspoon), and onion powder (1 teaspoon). In a shallow bowl, combine the flour (1/4 cup) and 2 tablespoons Parmesan cheese. Lightly dredge each chicken breast in the flour mixture, shaking off any excess.
Brown the chicken: Heat the olive oil (1 tablespoon) and butter (2 tablespoons) in a large skillet over medium-high heat. Add the chicken and cook until deeply golden on both sides and the internal temperature reaches 165°F (74ºC), about 4 to 5 minutes per side. Transfer to a plate and tent loosely with foil.
Build the flavor base: Reduce the heat to medium. Add the sun-dried tomato oil (1 tablespoon) and shallot (1) to the skillet. Cook until softened, about 2 to 3 minutes. Stir in the garlic (6 cloves) and cook for 30 seconds, just until fragrant. Add the tomato paste (1 tablespoon) and cook, stirring constantly, for about 1 minute, until it darkens slightly.
Deglaze the pan: Pour in the white wine (1/2 cup) and scrape up all the browned bits from the bottom of the skillet. Simmer until the wine has reduced by about half.
Create the sauce: Stir in the chicken broth (1 1/4 cups), Better Than Bouillon (1 heaping teaspoon), Parmesan rind (1), sun-dried tomatoes (3/4 cup), and red pepper flakes (1/2 teaspoon). Bring to a gentle simmer and cook for about 5 minutes to allow the flavors to meld.
Make it creamy: Reduce the heat to low. Whisk in the softened cream cheese (4 ounces) until completely smooth. Stir in the heavy cream (1 1/2 cups) and Parmesan cheese (1 cup), whisking until the cheese has melted. Simmer gently for 4 to 5 minutes, stirring occasionally, until the sauce thickens slightly.
Finish the chicken: Return the chicken and any accumulated juices to the skillet. Spoon the sauce over the chicken and simmer gently for 3 to 5 minutes, or until the chicken is heated through and coated in the sauce.
Finish the dish: Remove and discard the Parmesan rind. Stir in the lemon juice, basil, and parsley. Taste and adjust the seasoning with additional salt and pepper, if needed.
Serve: Spoon plenty of the creamy sauce over each chicken breast and garnish with additional Parmesan and fresh basil (1/4 cup). Serve immediately over mashed potatoes, buttered noodles, pasta, rice, or with warm crusty bread.