Preheat oven to 375°. Cut bread in half lengthwise; carefully hollow out top and bottom, leaving 1/2-in. shells (discard removed bread or save for another use). Spread 3 tablespoons butter and all of the mayonnaise inside bread shells. Line bottom bread shell with ham; top with tomato and onion.
In a large skillet, melt remaining butter; add eggs. Cook over medium heat, stirring occasionally until edges are almost set.
Spoon into bottom bread shell; top with cheese. Cover with bread top. Wrap in greased foil. Bake 15-20 minutes or until heated through. Cut into serving-size pieces. Yield: 6-8 servings.