Whisk the flour together with 2 tablespoons salt and 2 tablespoons pepper in a mixing bowl; set aside. Beat the eggs in a separate mixing bowl; whisk in the milk, 1 teaspoon salt, and 1 teaspoon pepper until smooth.
Heat oil in a deep-fryer or large saucepan to 375 degrees F (190 degrees C).
Dip the cucumber slices into the beaten egg, then press into the flour. Gently place the cucumber slices into the hot oil and cook until golden brown on both sides, about 3 to 4 minutes.
Drain on a paper towel-lined plate, allowing to cool 5 minutes before serving.
