Preheat oven to 425 degree F. Place a steamer basket in a 4-quart Dutch oven. Add water just below the bottom of the steamer basket; bring to boiling. Add broccoli. Cover and reduce heat. Steam for 4 to 5 minutes or until crisp-tender.
Meanwhile, cook lasagna noodles according to package directions. Drain noodles; rinse with cold water. Drain well. In a small bowl stir together ricotta cheese, the 1/4 cup Parmesan cheese, egg, and parsley; set aside
In a blender container or food processor bowl, blend or puree the roasted red peppers until almost smooth; set aside. In a large skillet, melt butter. Stir in flour and garlic. Cook and stir 1 minute. Gradually add milk and pureed peppers. Cook and stir until thickened and bubbly. Stir in salt, basil, and pepper.
Lightly coat a 13x9x2-inch baking dish or 3-quart rectangular casserole with nonstick cooking spray. Spread 3/4 cup of the sauce in dish. Arrange 3 lasagna noodles over sauce. Carefully spread 1/3 of the ricotta mixture over noodles. Top with 1/3 of the broccoli and sprinkle with 1/2 cup of the Monterey Jack cheese. Repeat layers 2 more times beginning with sauce. Top with remaining noodles and sauce.
Bake, covered, 20 minutes. Uncover and sprinkle with remaining 1/2 cup Monterey Jack cheese and the 3 tablespoons Parmesan cheese. Bake 10 minutes or until heated through. Let stand 10 minutes. Makes 10 main-dish servings.