Season each steak on both sides with a pinch of salt and of freshly ground black pepper, rubbing them into the meat. One at a time, dredge the steaks into the flour, then in the egg, then in the cracker crumbs. Reserve 1/4 cup of the flour.

In a large heavy skillet over medium heat, warm the corn oil. Add the steaks and cook them, turning them carefully once or twice, until the meat is fully cooked through and the crumb coating is brown and crisp, 8 to 10 minutes total. Transfer them to a platter and keep them warm.

Pour all but 4 tablespoons of the fat in the skillet through a strainer and discard it. Return any cracklings from the strainer to the skillet and set it out over low heat. Whisk the reserved 1/4 cup of flour into the fat in the skillet and cook over low heat, stirring and scraping, for 2 minutes. Gradually whisk in the milk. Raise the heat slightly and bring the gravy to a simmer. Cook, stirring often and scraping the browned deposits from the bottom of the skillet, until the gravy has thickened, 5 to 6 minutes. Adjust the seasoning.

Arrange the steaks on each of 4 plates. Spoon the mashed potatoes next to the steaks and nap both generously with gravy. Serve immediately.