Preheat the oven to 425 degrees F. Heat 1 tablespoon olive oil in a large pot over medium heat. When the oil shimmers, add the zucchini and season with salt and pepper. Cook until the zucchini is golden, 5-8 minutes. Remove the zucchini from the skillet and set aside.To the skillet, add the remaining oil and the onion. 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, garlic, 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 zucchini back to the skillet. Add the cayenne and a large pinch each of salt and pepper. Bring to a boil, cover, and reduce heat to low. Cook, covered for 15-20 minutes, until the rice is mostly cooked.Once the rice is cooked, stir in 1/2 cup of the Havarti and 1/2 cup of the cheddar. If needed, transfer the rice to an oven-safe casserole dish. Scatter the remaining 1/4 cup of each cheese overtop the casserole. Sprinkle on the everything spice and chives.Transfer to the oven and bake 10-15 minutes, until the cheese is melted. Switch the oven to broil and broil 1-2 minutes, until the cheese on top is becoming crispy. Serve warm with fresh basil.