Heat the olive oil in a large skillet over medium heat. Season the chicken breasts with salt and black pepper. Add the chicken to the skillet and cook for about 6-7 minutes on each side, or until the chicken is cooked through and no longer pink in the center. Remove the chicken from the skillet and set aside.
In the same skillet, add the minced garlic and sauté for about 30 seconds until fragrant. Pour in the heavy cream and bring to a gentle simmer.
Stir in the grated Parmesan cheese, chopped basil, lemon juice, and dried Italian seasoning. Cook for 2-3 minutes, stirring frequently, until the sauce thickens slightly.
Return the cooked chicken to the skillet, coating it with the basil cream sauce. Let it simmer for an additional 2-3 minutes to heat through.
Serve the chicken warm, drizzled with extra sauce, and garnish with additional basil if desired.