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.
Place marinated chicken onto the hot grill and discard the marinade. To avoid flare ups, place chicken pieces between the burners as opposed to directly over the flame. Cover the grill and cook for 2 to 3 minutes, until dark grill marks appear. Flip and cook on the other side for 2 to 3 minutes. Continue flipping and cooking until the internal temperature of the chicken reaches 165 degrees F. If certain drumsticks are cooking faster than others, move them to the side or the back of the grill so that they continue cooking slowly over indirect heat.