Steam broccoli florets until just tender, about 3 minutes; set aside. Preheat broiler. Butter 13x9x2-inch broilerproof baking dish. Heat 2 tablespoons olive oil in heavy large Dutch oven over medium-high. Working in batches, saute chicken strips until just cooked through, about 4 minutes. Transfer chicken strips to bowl. Add sliced red bell pepper to Dutch oven and saute until just tender, about 5 minutes. Add whipping cream, 1 cup grated Parmesan cheese and all of Monterey Jack cheese. Simmer until sauce thickens slightly, about 5 minutes. Add chicken strips and any juices in bowl to sauce. Add freshly cooked pasta and steamed broccoli florets and toss until sauce coats mixture, about 3 minutes. Season to taste with salt and pepper. Transfer pasta mixture to prepared baking dish. Sprinkle remaining 1/2 cup grated cheese over. Broil until just golden on top, about 3 minutes, and serve. Serves 4. Bon Appetit February 1995