Place the cornstarch in a medium saucepan. Whisk in 1 cup of the milk and keep stirring until the cornstarch is completely dissolved. Stir in the remaining 2 cups of milk and 1/2 cup of the sugar. Split the vanilla beans lengthwise and scrape the little seeds into the mixture. Over high heat, bring the mixture to a boil, stirring constantly. Stir for 1 or 2 minutes, until the mixture thickens heavily. Remove the vanilla beans and wash and dry them for another use. Pour the mixture into a shallow glass baking dish (about 8inches square) and smooth the top with a spatula until even. Cover and refrigerate for 4 hours, until quite firm.
With a knife dipped into hot water, cut the custard into approximately 11/4 inch squares. Dip the squares first into the beaten egg and then in the bread crumbs. Place the prepared squares onto a sheet of waxed or parchment paper.
In a heavy 10 to 12 inch skillet, heat the butter and oil over medium heat. When the foam begins to subside, add half of the custard squares and brown for about 2 minutes on each side, turning them over carefully with a large metal spatula. Transfer to a warm serving platter and cook the remaining squares in the same way. Serve, sprinkled with the remaining tablespoon of sugar and the cinnamon.
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