Heat oil in a medium saucepan over medium-high heat. Add flour and garlic; cook, stirring constantly, until fragrant, about 1 minute. Add broth and bring to a boil over high heat. Cook, whisking occasionally, until reduced by half, about 5 minutes. Reduce heat to medium-low. Slowly whisk in half-and-half. Add basil sprig and cook, stirring often, until thickened, about 8 minutes. Remove from heat; discard basil sprig. Stir in chopped basil, Parmesan, salt and pepper.Advertisement
To make ahead: Refrigerate for up to 2 days.