Using a small skillet, fill about 1/4 with extra-virgin olive oil and let heat on medium-high heat.
Meanwhile, set up breading station using a small to medium bowl for the eggs, one plate with Italian bread crumbs and another plate for the Panko crumbs. Salt tomato slices with garlic salt and dip into egg mixture then in Italian bread crumbs. Dip the tomato in the egg mixture once more and then into the Panko crumbs. Repeat until all tomato slices are breaded.
Place one to two tomatoes into the oil and fry for 1 to 2 minutes and gently turn the tomatoes over using tongs. Allow to cook for 1 to 2 minutes longer or until golden brown.
Drain on paper towels and garnish with shredded mozzarella cheese or freshly grated Parmesan cheese.