Position racks in the upper and lower thirds of the oven and preheat to 425 degrees . In a small bowl, whisk 3 tbsp. EVOO with the mustard, garlic and lime juice. Transfer 3 tbsp. of the mustard dressing to a large bowl. Add the potato wedges; season with salt and pepper and toss to coat. Place the chicken, skin side up, on a foil-lined baking sheet. Rub with the remaining dressing; season. Surround with the potatoes and roast on the lower rack, 40 minutes.
On another baking sheet, toss the kale with the remaining EVOO; season. Transfer the chicken to the upper rack and place the kale on the lower rack. Roast until the chicken is cooked through and the kale is crispy, 20 minutes. Let the chicken rest for 5 minutes, then serve with the kale and potatoes.