Sprinkle chicken evenly with salt and pepper. Heat 1 tablespoon butter in a large nonstick skillet over medium heat until bubbling. Add the chicken; cook until browned and cooked through, about 3 minutes per side. Transfer the chicken to a plate and cover to keep warm.
Return the pan to medium heat. Add the remaining 1 tablespoon butter and swirl to coat. Add garlic; cook, stirring constantly, until fragrant, about 1 minute. Add broth and bring to a boil over medium-high heat. Add cream cheese; cook, stirring constantly, until melted and thickened, about 5 minutes. Stir in lemon slices and basil. Return the chicken and any accumulated juices to the pan; simmer over medium heat until the sauce thickens and coats the chicken, about 4 minutes.
