A traditional pesto infuses these drumsticks with fantastic flavor during grilling. Create seasonal variety by adding different herbs and nuts to the pesto and serving with different vegetable side dishes.
Combine all pesto ingredients except 1 cup olive oil in food processor. Finely chop, then gradually add oil until well mixed; set aside.
Prepare grill. Coat drumsticks with 1 tablespoon olive oil; add salt and pepper. Grill over medium hot coals for 15 to 20 minutes turning occasionally. Brush drumsticks with ¼ cup of pesto. Cook for 5 to 10 minutes longer or until chicken is no longer pink.
Serve with extra pesto. Refrigerate pesto to toss with salads or eggs, or to serve with tomatoes.
Nutritional values may change if you choose to substitute another chicken product.