Slice or pound the chicken breasts to about 1/2-inch thickness so they cook evenly; season both sides with 1/2 teaspoon salt and 1/4 teaspoon pepper.
Heat 1 tablespoon olive oil in a large skillet over medium-high heat. Add the chicken and cook 4–5 minutes per side until mostly cooked through and golden; transfer to a plate and set aside.
Reduce heat to medium and add 3 tablespoons butter to the same skillet. When melted, sauté 2 teaspoons minced garlic for about 30 seconds until fragrant.
Stir in 3 tablespoons flour to form a paste and cook 1 minute while stirring to remove the raw flour taste.
Whisk in 1 cup chicken broth and 3/4 cup heavy cream until smooth, then add 1/2 cup grated Parmesan; stir until the sauce is combined.
Add 1/2 cup drained sun-dried tomatoes and 1 teaspoon dried Italian seasoning; season with additional salt and pepper to taste and simmer a few minutes until the sauce thickens slightly.
Return the chicken to the skillet, nestling it into the sauce. Reduce heat to medium-low and simmer uncovered 8–12 minutes until the chicken is cooked through and the sauce has thickened.
Garnish with chopped fresh basil and serve warm over pasta or rice if desired.