Preheat the oven to 400°F.
Heat the olive oil in a small saucepan. Add the garlic and oregano and cook for 1 minute, until fragrant. Add a pinch of chile flakes and cook for 1-2 minutes. Stir in the crushed tomatoes and bring to a simmer for 20 minutes. Season with salt and pepper.
Place the flour, eggs and breadcrumbs into three separate bowls. Season each with salt and pepper. Bread the eggplant by first dipping it in the flour, flipping to coat both sides. Then dip it in the eggs, and finally the breadcrumbs. Place the breaded eggplant on a baking sheet.
Heat 1 inch of oil in a skillet and heat to 375°F. Fry the eggplant, working in batches and flipping halfway through. They’re done when the breading is golden brown. Transfer to a paper towel-lined plate.
Bring a large pot of salted water to a boil for the broccolini. Prepare an ice bath by filling a large bowl with water and ice. When the water boils, add the broccolini for 2-4 minutes, until bright green and crisp-tender, then immediately transfer to the ice bath to stop the cooking process. Remove from the ice bath after 1-2 minutes.
In a bowl, combine the mozarella, ricotta and pecorino cheese.
Layer the fried eggplant, sauce and cheese in a baking dish. Bake for 10 minutes, or until hot and the cheese is melted.
Divide the eggplant parm between plates and top with blanched broccolini.