Preheat oven to 400 degrees F.
Wash potatoes well. Pat dry with paper towel. Peel if desired, otherwise cut into chunks (about 1/2 thick).
Cut chicken into bite size pieces.
Slice kumquats thinly.
Brush large sheet pan with olive oil. Arrange potato chunks in a single layer. Roast for 7 to 8 minutes. Drizzle with 1 tablespoon of olive oil and gently toss together.
Add chicken and broccoli to pan, arranging pieces in between the potato chunks.
Arrange slices of kumquats on top of chicken and vegetables.
Drizzle everything with remaining olive oil. Season with salt and pepper.
Roast in oven for 18 to 20 minutes OR until the chicken registers internal temperature of 165 degrees F. Remove from oven and let sit for 10 minutes.
Garnish dish with fresh chopped basil.