Preheat oven to 450 degrees. Slice top 1/2 inch from tomatoes and scoop out flesh (reserve for another use; see below). In a medium skillet, heat 2 teaspoons oil over medium. Add corn and scallion whites and cook until crisp-tender, 3 minutes. Transfer to a medium bowl and stir in jalapeno, beans, 1/4 cup cheddar, 1/2 cup breadcrumbs, and lime juice. Season with salt and pepper.
Coat an 8-inch square baking dish with 1 teaspoon oil. Brush tomato skins with 1 teaspoon oil, season all over with salt and pepper, and place in dish. Fill tomatoes with corn mixture. Combine remaining 1/4 cup cheddar, 1/2 cup breadcrumbs, and 2 teaspoons oil, season with salt and pepper, and divide among tomatoes. Tent dish loosely with foil and bake 10 minutes. Uncover and bake until tomatoes are soft and breadcrumbs are deep golden, about 5 minutes more.