Prepare the Dough: In a large bowl, combine the warm water, yeast, and granulated sugar. Stir and let sit for 5 minutes until frothy. Add the pumpkin puree, salt, and pumpkin pie spice to the yeast mixture. Stir to combine. Gradually add the flour, 1 cup at a time, mixing until a dough forms. Knead the dough on a floured surface for about 5 minutes, until smooth and elastic. Place the dough in a greased bowl, cover with a damp cloth, and let rise in a warm place for about 1 hour, or until doubled in size.
Shape the Pretzels: Preheat your oven to 450°F (230°C). Line a baking sheet with parchment paper. Punch down the risen dough and divide it into 10 equal pieces. Roll each piece into a long rope, about 18 inches long, and shape into a pretzel.
Prepare the Baking Soda Bath: In a large pot, bring the 10 cups of water and baking soda to a boil. Carefully dip each pretzel into the boiling water for about 30 seconds, then remove with a slotted spoon and place on the prepared baking sheet.
Bake the Pretzels: Brush each pretzel with the beaten egg to give them a golden color. Bake in the preheated oven for 12-15 minutes, or until golden brown
Cinnamon-Sugar Topping: In a small bowl, mix the granulated sugar and ground cinnamon. Sprinkle the cinnamon-sugar mixture over the warm pretzels.
Prepare the Glaze: In a medium bowl, whisk together the powdered sugar, milk, and vanilla extract until smooth. Drizzle the glaze over the cooled pretzels.
Cool and Serve:Allow the pretzels to cool slightly on a wire rack before serving.