In a heavy 3 to 4-quart saucepan melt the butter over moderate heat. When the foam begins to subside, stir in 3/4 cup of the flour and mix well. Add the milk in a stream whisking constantly. Cook over high heat until the sauce comes to a boil and thickens. Simmer for another 10 minutes on low heat, whisking often.
Take the pan off the heat and beat in the egg yolks, one at a time, using a wooden spoon. Season with the salt and pepper. Add the grated cheese and mix well. Pour into a greased baking dish (8 by 6-inches) and spread into a 1/2-inch thick layer. Use a spatula to smooth the top. Allow to cool to room temperature, cover with plastic wrap, and refrigerate for 8 hours, or overnight, until firm.
Using a pastry wheel or a sharp knife, cut the mixture into 2-inch squares and transfer them to a sheet of waxed paper. Dredge each square into the remaining flour and coat completely. Shake off excess flour and dip into the egg wash, followed by the bread crumbs. Pat the square gently with a spatula to help the crumbs adhere. Repeat with all the squares and place them on a baking sheet. Refrigerate for at least 1 hour, until the coating is firm.
In a deep fryer or heavy saucepan, heat 2 to 3-inches of oil until it reaches 375 degrees. Preheat the oven to its lowest temperature. Line a baking dish with paper towels and set in the middle of the oven.
Deep-fry the squares 3 or 4 at a time, turning them with a slotted spoon for about 5 minutes, until golden brown on both sides. As they brown, transfer them to a baking dish in the oven to keep them warm while you deep-fry the rest. Serve at once as a first course or an accompaniment to the drinks.