Heat oven to 350 degrees. Lightly brush a 3-quart baking dish with 1 teaspoon olive oil; set aside. Heat 1 tablespoon olive oil in a Dutch oven over medium heat. Add leeks; cook slowly until tender, about 5 minutes. Remove leeks; drain in a colander. Transfer to a medium bowl to cool. Add 1 tablespoon olive oil to Dutch oven; repeat cooking and draining process with celery. Add 1 tablespoon olive oil to Dutch oven, and repeat cooking and draining process with Swiss chard.
In a large bowl, combine the eggs, 1/2 cup Parmigiano-Reggiano, cream, ricotta, Aleppo pepper, and 2 tablespoons olive oil. Season with salt and black pepper. Whisk until well combined.
Add cooked vegetables to egg mixture; thoroughly combine. Pour into prepared baking dish. Spread evenly; cover with foil. Pull a rack out of the oven, and set a roasting pan on top; fill pan with 2 inches warm water. Place baking dish in roasting pan; slide rack back into oven. Bake 40 minutes. Uncover; continue baking until set, about 20 minutes.
Heat broiler. Sprinkle remaining 1/2 cup Parmigiano-Reggiano over the tortino. Place under broiler until lightly browned. Cut into squares, and serve warm.
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