Grate the zest of 1 lemon and set aside; juice both lemons. Combine the garlic and olive oil in a large microwave-safe bowl and microwave until the garlic starts sizzling, 1 to 2 minutes; let cool. Add the lemon juice, herb sprigs, 1 teaspoon each salt and pepper, and the chicken wings. Using your hands, rub the wings with the oil mixture; firmly press the wings down, making sure they are covered with some of the herbs and garlic. Cover and refrigerate at least 4 hours or overnight, stirring once or twice.
Meanwhile, pulse the butter, basil leaves, lemon zest and 1/2 teaspoon each salt and pepper in a mini food processor until combined. Cover and refrigerate until ready to use.
Preheat a grill to medium high and prepare for indirect grilling: On a charcoal grill, bank the coals to one side; on a gas grill, turn off half the burners. Remove the basil butter from the refrigerator. Remove the wings from the marinade. Brush the grill grates with olive oil and place the wings on the cooler side of the grill (indirect heat). Cover the grill and cook, turning the wings once, until almost completely cooked through and the skin is beginning to crisp, about 30 minutes. Move to direct heat and grill, turning often, until the skin is crisp and lightly charred, 10 to 15 more minutes.
Transfer the wings to a large bowl. Add the basil butter and toss to coat. Add the parmesan and season with salt and pepper; toss again. Serve with lemon wedges.