Preheat a large, heavy skillet over med-high heat.
Put steaks on wax paper-lined work surface and cover with another piece of wax paper. Pound steaks to 1/4 inch thickness. Set steaks aside.
Line work surface with more wax paper and pour 1/2 cup flour into each of two piles on opposite ends of this work space. Add cornmeal, paprika, salt and pepper to one pile of flour.
Beat eggs and water in a shallow dish or pie plate.
Cut steaks into 4 portions and coat first in the plain flour, then in egg, and then in the seasoned flour and cornmeal mixture.
Add 2 T of oil to the hot skillet and brown 2 steaks at a time. As they brown, remove from the pan and add more oil as needed. When the last 2 portions are browned, add the first two back to the pan. Cover pan and lower heat to med-low and cook covered for 15 minutes.
Remove steaks to a serving platter and pour off all but 2-3 T. of the drippings. Add 2 T of flour to the drippings and cook for 2 minutes. Whisk in broth and season with salt and pepper. Add half and half or cream and whisk into gravy. When the gravy bubbles, remove from heat.