Meanwhile, heat the remaining 1 Tbsp. oil in a small saucepan over medium heat. Add onion and cook, stirring often, until softened, 3 to 4 minutes. Add garlic; cook, stirring, until fragrant, about 30 seconds. Add broth, mustard, and wine (if using); simmer, stirring often, until slightly reduced, 2 to 3 minutes. Stir in Parmesan, parsley, and the remaining 1 1/2 tsp. fresh thyme (or 1/2 tsp. dried).