Pat the chicken breasts dry with paper towels. Season all over with 1 teaspoon of the salt. Heat the oil in a large skillet over medium-high heat. Once the oil is glistening, add the chicken and cook, undisturbed, until golden brown, about 5 minutes per side. Transfer to a plate.

Reduce the heat to medium and add the garlic to the same skillet. Cook, stirring, until fragrant, about 30 seconds. Stir in the heavy cream, chicken stock, bouillon, ¼ cup of the Parmesan cheese, sun dried tomatoes, Italian seasoning, black pepper, red pepper flakes (if using), and remaining ½ teaspoon salt. Whisk until combined and smooth.

Return the seared chicken to the skillet, nestling it into the sauce. Bring to a simmer, then reduce the heat to medium-low. Cook until the sauce has thickened slightly and the internal temperature of the chicken reaches 165°F on an instant-read thermometer, about 8 to 10 minutes.

Remove from heat and top the chicken with the fresh basil and remaining ¼ cup Parmesan cheese. Sprinkle with additional red pepper flakes, if desired. Serve over pasta or mashed potatoes, if desired.