Combine potatoes, carrots and water. Cover and cook until vegetables are tender.
Fry bacon until crisp. Drain bacon; crumble into bits and set aside, saving 3 tablespoons bacon drippings. Add onion to drippings; sauté until tender but not brown.
Blend in flour; salt and pepper. Add milk, half and half, vegetables and vegetable liquid. Cook and stir until the sauce is smooth and thickened.
Add corn; heat through. Just before serving sprinkle with bacon.
Spread 4 slices bread with butter. Place in bottom of greased 8-inch square baking dish. Toast lightly in oven (350° F) about 10 minutes. While bread is toasting, brown bacon, onion, celery and green pepper. Season with salt. Place 4 slices cheese on each of 4 toast slices in baking dish. Arrange bacon mixture over cheese. Place a tomato slice on each sandwich. Top with remaining cheese slices. Cover with remaining bread slices. Combine eggs, milk and mustard, mixing well. Pour over sandwiches. Bake in moderate oven (350° F) about 40 minutes.
