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In a large mixing bowl, combine the warm water, sugar, and kosher salt. Sprinkle the yeast on top and let it sit for 5 minutes until it becomes foamy.
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Add the flour and melted butter to the mixture and stir until a dough forms. Knead the dough on a floured surface for 5-7 minutes until it becomes smooth.
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Place the dough in a greased bowl, cover it with a damp towel, and let it rise for 1 hour.
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Preheat the oven to 450°F and line a baking sheet with parchment paper.
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In a large pot, bring 10 cups of water and baking soda to a boil.
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Divide the dough into 12 equal pieces and roll each piece into a long rope. Shape the dough into a Mickey Mouse head by making a circle for the head and two smaller circles for the ears.
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Carefully drop each pretzel into the boiling water mixture for 30 seconds on each side. Remove with a slotted spoon and place on the prepared baking sheet.
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Brush each pretzel with beaten egg and sprinkle with coarse salt.
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Bake the pretzels for 12-15 minutes until golden brown.
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Let the pretzels cool for a few minutes before serving.