Rinse and pat dry the wings. Place them in a large container or plastic baggie. (You may have some extra marinade that you can freeze for later use rather than pouring it all on the wings).
Place the basil, garlic, olive oil, lemon juice, salt, and pepper in a food processor and blend until smooth. Pour the mixture over the wings and toss to coat.
Seal the bag or cover the dish and place in the refrigerator for 1 to 4 hours.
Allow the wings to sit out of the refrigerator for about 20 minutes before grilling.
Preheat your Foreman Grill until hot.
Place as many wings as will fit on the grill without crowding too much. Close the lid and grill for 10 minutes.
Flip them over, close the lid, and grill for another 10 minutes.
Check the internal temperature with a meat thermometer at 20 minutes. You want it to read at least 165°F. If it is lower than that, grill for another 2 to 5 minutes or so until the temperature is reached.
Remove the wings to a platter and dust with the parmesan cheese.
Repeat until all the wings are cooked.