Slice the green tomatoes into uniform ¼-inch thick rounds.
Prepare your dredging station.
In a shallow dish, whisk together the egg and heavy cream.
In a second shallow dish, stir together the coconut flour, Parmesan cheese, salt, and pepper.
Heat approximately ½ inch of oil in a large, heavy-bottomed skillet over medium to medium-high heat until it shimmers, reaching about 350°F (175°C).
Dip each tomato slice first into the egg mixture, letting any excess drip off.
Then, press the slice firmly into the flour mixture, coating both sides completely.
Working in small batches to avoid overcrowding the pan, carefully place the coated tomato slices into the hot oil.
Fry for 2-3 minutes per side, until they are a deep golden brown and crispy.
Transfer the fried tomatoes to a wire rack to drain.
Sprinkle immediately with a little extra salt.
Serve hot and enjoy!