Place tenderized cube steaks in a shallow dish.
Whisk together 2 eggs, 1/4 cup milk, 1/2 teaspoon salt, and 1/2 teaspoon pepper.
Combine 1 1/2 cups flour with 1/2 teaspoon salt and 1/2 teaspoon pepper in another shallow dish.
Coat steaks in egg wash, then dredge in flour mixture.
Heat 1/2 cup oil in a large skillet over medium heat until shimmering.
Fry steaks 2-3 at a time until golden brown on both sides (3-4 minutes per side). Transfer to paper towels to drain.
In the same skillet, melt 4 tablespoons butter.
Mix in 1/2 cup flour until smooth, then gradually whisk in 4 cups water or beef broth.
Simmer until thickened, adding milk for creaminess.
Stir in cayenne pepper (if using) and season with remaining salt and pepper.
Serve steaks hot with gravy and optional green onions over biscuits, rolls, or cornbread.