Prep Time: 60 minutes
Bring a large pot of salted water to a boil over a high flame. Score a small X into the bottom of each tomato and place in the boiling water. Blanch for 1 minute. Remove the tomatoes with a slotted spoon and place them in a large bowl filled with ice water until cool to the touch. Gently peel with a small knife, starting at the X. Puree the peeled tomatoes in a blender or food processor until smooth. Alternately, smash with a potato masher for a chunkier sauce.
Heat the olive oil in a sauté pan over a medium flame until hot. Add the garlic and stir until fragrant, about 30 seconds. Add the tomatoes and stir. Season with a pinch of salt and pepper to taste. Bring to a boil and and then reduce to a simmer, until slightly thickened, about 20 minutes. Set aside until cool.
While the tomato sauce is cooking, slice the eggplant into 1/2" rounds. Sprinkle with salt and place in a strainer in a bowl. Let sit for 10 minutes or more. Meanwhile, set up a frying station. Using 3 bowls, place the flour, eggs and breadcrumbs separately into each. Season the flour and breadcrumbs with a pinch of salt and pepper. Scramble the eggs with a fork. Preheat the oven to 400 degrees.
In a large frying pan, heat 1/4" oil over a medium flame until hot. Begin breading the eggplant by dredging each piece in flour. Shake off any excess and then dip into the egg and then the breadcrumbs, until covered. Continue until all the pieces are breaded. Add to the hot pan of oil and cook until golden brown all over, about 5 minutes each side. Remove to a plate lined with paper towel.Place the eggplant into a large casserole dish and top with the tomato sauce. Dot with chunks of burrata and season with a pinch of salt and pepper. Place into the oven and cook until the cheese is melted and bubbly, about 20 minutes. Divide among 4 plates and garnish with remaining oregano.