In a saucepan over medium heat, melt butter. Add minced garlic & sauté for 1 minute until fragrant. Whisk in the flour & cook for 2 minutes. Gradually pour in warm milk & pesto, whisking constantly to prevent lumps. Simmer gently for 5-7 minutes until the sauce thickens enough to coat the back of a spoon. Remove from heat. Stir in fresh dill & salt & pepper to taste. Set aside.