Preheat the oven to 425 degrees F. Heat the olive oil in a large pot over medium heat. When the oil shimmers, add the onion and carrot and cook until fragrant, about 5 minutes. Stir in the chicken and season with salt and pepper. Cook until the chicken is seared, 2-3 minutes. Add the butter, rice, orzo, and thyme, and cook until golden and toasted, 2-3 minutes. Add the broth and bring to a boil over high heat. Add the broccoli, bay leaves, garlic powder, cayenne, and a large pinch each of salt and pepper. Bring to a boil, cover and reduce heat to low. Cook, covered for 20-25 minutes, until the rice is mostly cooked.Once the rice is cooked, stir in the lemon zest, milk, and 1/2 cup of cheese. If needed, transfer the rice to an oven-safe casserole dish. Scatter the remaining cheese over top the casserole. Transfer to the oven and bake 15-20 minutes, until the cheese is melted and just beginning to brown. Serve warm with additional thyme and fresh basil.