Combine 1/2 cup of bread crumbs and 1/4 cup Parmesan cheese; set aside. Cut a thin slice off the top of each tomato; scoop out pulp and place in a strainer to drain. Place tomatoes upside down on paper towels.
Cook the broccoli until crisp-tender; drain. Chop tomato pulp and place in a large bowl. Add broccoli, cheddar cheese, mayonnaise, salt, pepper and remaining crumbs and Parmesan; mix gently.
Stuff tomatoes; place in a greased 11x7-in. baking dish. Sprinkle with reserved crumb mixture. Bake, uncovered, at 375° for 30-40 minutes.