Directions. 1  In a heavy-bottom 4-quart pot, heat butter and olive oil over medium heat. Saute leeks 5-7 minutes, until tender. 2  Add cucumber and chicken stock. Simmer until cucumber is softened (about 6-8 minutes). 3  Pour small batches of cucumber soup into a blender and puree until smooth.
Grill for 5-10 minutes, depending on how hot the grill is (you do not want the chicken to burn). Once you have a good sear on one side, move the chicken pieces to the cooler side of the grill.
For a gas grill, preheat grill. Reduce heat to medium. Adjust for indirect cooking. Test for medium heat above the drip pan. Place drumsticks on the grill rack over drip pan. Cover and grill for 50 to 60 minutes or until chicken is no longer pink (180 degrees F), turning once halfway through grilling.tep 3: Grill the chicken. Cover and grill for 25 minutes. Turn chicken over. Cover and grill for 25 to 30 minutes more or until juices run clear and an instant-read thermometer inserted in thickest part of thigh registers 180 degrees F. Remove chicken from grill and let rest for 10 minutes.