Slice tomatoes 1/2 inch thick. Discard the ends.
Whisk eggs and milk together in a medium-size bowl. Scoop flour onto a plate. Mix cornmeal, bread crumbs and salt and pepper on another plate. Dip tomatoes into flour to coat. Then dip the tomatoes into milk and egg mixture. Dredge in breadcrumbs to completely coat.
In a large skillet, pour vegetable oil (enough so that there is 1/2 inch of oil in the pan) and heat over a medium heat. Place tomatoes into the frying pan in batches of 4 or 5, depending on the size of your skillet. Do not crowd the tomatoes, they should not touch each other. When the tomatoes are browned, flip and fry them on the other side. Drain them on paper towels.