If using wooden skewers, soak them in a casserole dish.
Whisk half of the dijon with the lemon zest, juice, and half of the olive oil. Cut the chicken into chunks and toss with the marinade. Set aside.
Place the potatoes in a pot of cold water, covered by about 2 inches. Bring up to a boil. Simmer for 12-15 minutes until the potatoes can be easily speared with a skewer.
Meanwhile, cut the cauliflower into large chunks, about 2 inches big. When the potatoes are cooked through, scoop out. Replace with the cauliflower and simmer for 2-4 minutes until the cauliflower is just barely “skewerable”.
Cut the onion into chunks. Toss all of the vegetables generously with the remaining olive oil, salt and pepper.
Heat the grill on high. Thread the chunks of chicken & veggies onto the sticks. Once they are all assembled, reduce the heat of the grill to medium-low. Line up on the grill and sear on each side for about 5-8 minutes until the chicken is cooked through.
While the chicken grills, whisk together the remaining Dijon with the mayonnaise and/or greek yogurt combination. Serve this alongside as a dipping sauce.