Clean the soft shell crabs by removing the face, gills, and apron. Pat them very dry with paper towels.
In a shallow bowl, whisk together the flour, cornstarch, baking soda, and kosher salt.
Whisk in the cold beer until the batter is smooth.
Heat the cooking oil in a large skillet, cast iron skillet, or deep fryer to 350 to 375°F.
Dip each crab into the batter, briefly letting the excess drip off.
Fry until golden brown and crisp, about 2 to 3 minutes per side.
Transfer to a wire rack or paper towel-lined plate and season right away with salt and black pepper.
Serve on a sandwich or over grits.