Pour vegetable oil into a large cast-iron skillet ( approx. a depth of 1/4 to 1/2 inches deep)
Heat to 375° degrees F. To test the heat, flick a few breadcrumbs into the oil. If the oil doesn't react/spit, it's not hot enough yet).
Lightly beat the eggs in one bowl; set aside.
Put the flour in it's own bowl; set aside.
Combine the breadcrumbs, sea salt, and ground black pepper; set aside.
Create a small assembly line next to your skillet, or as close by as you can, so you can dredge your tomato slices and place them in the skillet with less of a mess.
Dredge each tomato slice in flour, followed by the egg, followed by the breadcrumb mixture.
Carefully place the tomato slices into the hot oil, in batches, cooking for 1-2 minutes per side or until golden brown on both sides.
Remove the golden slices with a slotted spoon and place them on paper towels or a rack to drain absorb/drain the oil.
Garnish with parsley if desired.
Serve hot with dipping sauce of your choice. If serving on their own, sprinkle with a bit of sea salt.