In a small bowl, combine yogurt, lemon juice, onion, garlic, ginger, garam masala, turmeric, cayenne, smoked paprika, and salt. Place the chicken thighs in a gallon freezer bag with the marinade and refrigerate for 1 hour up to overnight.
When ready to cook, adjust an oven rack in the center and another 4 to 6 inches from the broiler. Preheat the oven to 425°F. Spray a large rimmed sheet pan with olive oil.
In a large bowl or on a plate, toss the carrots and cauliflower with olive oil. Sprinkle with garam masala, salt, and black pepper to taste and toss to coat. Spread the vegetables onto the pan. Remove the chicken from the marinade, scrape off the excess, and nestle the chicken thighs in with the vegetables. Lightly spray with olive oil.
Roast on the center rack until the vegetables are tender and the chicken is cooked through, about 30 minutes.
In a small bowl, combine yogurt, lemon juice, garlic, cilantro, and salt.
Switch the oven to broil. Move the pan to the higher rack and broil until the chicken and vegetable are slightly charred, about 3 to 5 minutes. Sprinkle with the chopped cilantro and serve with the yogurt sauce on the side.
