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 cook until fragrant, about 5 minutes. Stir in the mushrooms and season with salt and pepper. Cook until softened, 2-3 minutes. Add the butter, orzo, broccoli, and thyme, and cook until golden and toasted, 5 minutes. Add the wine, broth, bay leaf, garlic powder, cayenne, and a large pinch each of salt and pepper. Simmer 8-10 minutes until the orzo is al dente, stirring often.Once the orzo is cooked, stir in the lemon zest, milk, and 1/2 cup of the cheddar. If needed, transfer the orzo to an oven-safe casserole dish. Scatter the remaining cheeses overtop of the casserole. 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 thyme and basil.