Adjust rack to top position and preheat oven to 425 degrees. Wash and dry all produce. Trim and peel carrots; cut on a diagonal into 1/2-inch-thick pieces. Zest and quarter lemon.

Toss carrots on one side of a baking sheet with a large drizzle of olive oil, salt, and pepper. Roast on top rack for 5 minutes. Meanwhile, pat chicken dry with paper towels. Season generously with salt and pepper; drizzle with olive oil. Once carrots have roasted for 5 minutes, remove from oven. Add chicken to opposite side of sheet from carrots. Continue roasting until chicken is cooked through and carrots are tender, 18-20 minutes.

Meanwhile, in a small pot, combine rice, 3/4 cup water (11/2 cups for 4 servings), and a pinch of salt. Bring to a boil, then cover and reduce to a low simmer. Cook until rice is tender, 15-18 minutes. Keep covered off heat until ready to serve.

Once chicken is cooked through, remove sheet from oven; transfer carrots to a plate. Heat broiler to high or oven to 500 degrees. Spread half the pesto onto tops of chicken, then sprinkle with mozzarella. Return to top rack and broil or bake until cheese is melty, 2-4 minutes.

Fluff rice with a fork; stir in 1 TBSP butter (2 TBSP for 4 servings) and lemon zest to taste. Season with salt and pepper.

Divide rice, chicken, and carrots between plates. Sprinkle with as many chili flakes as you like. Serve with lemon wedges and remaining pesto on the side for dipping.