In a pie plate, whisk the egg with the milk. In another pie plate, generously season the flour with salt and pepper. Dredge the beef in the flour, tapping off the excess. Dip the coated slices in the beaten egg mixture and dredge again in the flour, lightly patting the coating to help it adhere.
In a large cast-iron skillet, heat 1/2 inch of vegetable oil until shimmering. Working in 2 batches, fry the steak over moderate heat, turning once, until golden and crispy, about 5 minutes. Drain on paper towels and season lightly with salt.
Pour the cooking oil into a heatproof cup and wipe out the skillet. Return 2 tablespoons of the oil to the skillet and add the onion, garlic and ginger. Cook over moderate heat, stirring occasionally, until the onion is softened and browned, about 5 minutes. Add the curry powder and Sriracha and cook, stirring, for 2 minutes. Add the coffee and boil until reduced by half, about 3 minutes. Add the coconut milk, lime juice and sugar, season the gravy with salt and pepper and simmer until thickened, about 5 minutes.
Put the chicken-fried steaks in shallow bowls. Top with the curry gravy and serve with lime wedges.