In a small bowl, combine the EVOO, 2 tbsp. lemon juice, 1/2 tsp. chili powder and 1/2 tsp. salt.
In a 9-by-13-inch baking pan, toss the carrots and 12 cloves garlic with 1/4 cup of the lemon-chili mixture. Place the pan in a cold oven and heat to 400 degrees .
Meanwhile, peel and grate the remaining 4 cloves garlic into a small bowl. Stir in 2 tbsp. lemon juice and the remaining 4 tsp. chili powder. Rub the garlic-chili paste evenly onto the chicken flesh under the skin; rub some over the skin, too. Let sit until the oven and pan are preheated.
Season the chicken with salt and pepper. Place the chicken, skin side up, over the vegetables in the baking pan. Roast until cooked through but still juicy, about 40 minutes.
In a salad bowl, toss the romaine and cilantro with the remaining lemon-chili mixture. Serve with the chicken.