Preheat oven to 400°F.
Warm 2 tablespoons olive oil in a 12-inch ovenproof skillet (preferably cast iron) over medium-high heat. Add the eggplant and quickly stir to coat it all in oil. If you don’t move quickly enough, all of the oil will soak into the first eggplant that touch it. Season with 1 teaspoon salt and stir in 2 tablespoons water and cook, stirring often, for 5 to 7 minutes, until eggplant is beginning to get tender and browned.
Stir in 1 thinly sliced leek, 4 minced garlic cloves, and 3/4 teaspoon dried oregano. If your skillet is very dry by this point, add another 1 tablespoon olive oil. Cook for 2 minutes, until the leek is softened.
Stir in 1 (28 ounce) jar of tomato sauce and 1/4 cup water and reduce heat to medium-low. Simmer for 5 minutes. If your sauce is bubbling and splattering, reduce the heat.
Meanwhile, in a small bowl, stir 1 1/2 cups breadcrumbs, 2 tablespoons olive oil, remaining 1/2 teaspoon oregano, and 1/2 teaspoon salt together until combined.
*OPTIONAL EXTRA CHEESY STEP: cube 8 ounces of fresh mozzarella cheese and poke the cubes down into the eggplant and tomato mixture.*
Use a spatula to smooth the eggplant tomato mixture, then sprinkle the breadcrumbs evenly over top.
Bake for 20 to 30 minutes, until the breadcrumbs are golden-brown.
Tear the burrata into 6 to 8 pieces and place over the breadcrumbs. Return the skillet to the oven for 3 minutes just to warm the burrata.
Sprinkle 1/4 cup fresh parsley or basil over top and enjoy!