In a blender add the olive oil, kumquats, basil, 1 teaspoon of pepper and 1 teaspoon salt and blend until smooth. Cut chicken into about 1 inch square bites and put in a glass container. Coat with the kumquat-basil marinade. Place in the refrigerator for up to 2 hours.
While chicken is marinating, parboil the potatoes for 6-8 minutes or until just fork tender. Drain and let all the water evaporate. This can be done the night before. Just before assembling kabobs. Drizzle them in olive oil, season with salt and pepper and toss to coat evenly.
To Assemble The Kabobs: Thread 2-3 pieces of chicken to one piece of potato. If the potatoes are too large cut them in half to match the size of the chicken pieces. Fill skewers no more than 3/4 of the way. Continue until you run out of chicken.
Under The Broiler: Place kabobs under the broiler until nicely browned and juices are running clear. You'll want to turn after about 6 minutes to cook both sides evenly.
On a preheated grill, place the skewers turning frequently until nicely browned on all sides (about 8 minutes per side). You may also cook the kebabs under the broiler. Serve along side the Roasted Red Pepper Dipping Sauce.
In a blender add the olive oil, kumquats, basil, 1/2 teaspoon of pepper and 1 teaspoon salt and blend until smooth. For extra flavor add a few tablespoons of the pan drippings from the skewers before you add the salt. Taste and adjust seasoning if needed.