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In a small bowl, combine the cinnamon and sugar for the topping. Set aside. Line a plate with paper towels and place a wire rack over a sheet pan. Set both aside.
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Combine the flour, sugar, baking powder, and salt in a large bowl. Add the melted butter and warm milk and stir until a slightly sticky dough forms. Cover the bowl with a piece of plastic wrap and let rest for 10 minutes.
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While the dough is resting, pour 2-3 inches of neutral oil (canola, vegetable, peanut, etc.) into a dutch oven or other heavy bottomed pot. Add an oil/candy thermometer to the side of the pot to monitor the temperature. Once it reaches 350 F, you're ready to fry the dough!
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After the 10 minute rest, transfer the dough to a lightly floured work surface. Divide the dough into 4 portions and roll it in the flour so that it's lightly covered and easier to handle. Shape each dough piece into a oval/rounded rectangle, reminiscent of a beaver tail. Flatten it to about 1/4 inch thickness. It doesn't have to be perfect!
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When the oil is at 350 F, place one beaver tail into the oil and fry for 1-2 minutes per side. Place the freshly fried dough on the paper towel lined plate. Once the excess oil has been absorbed, transfer the dough to the wire rack and sprinkle a few spoonfuls of the cinnamon sugar mixture on top of it. Repeat with remaining dough pieces.
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You can either enjoy the beaver tails as is, or you can top with a drizzle of Nutella and/or slices of banana!