In the bowl of a stand mixer, combine the yeast, beer, and brown sugar. Let sit 5-10 minutes until very frothy.
Stir in the melted butter and pumpkin puree. Attach the bread hook to your mixer. Add 2 cups of flour, the cinnamon, and ginger, and begin stirring on low speed. Add 1 cup more and knead until a tacky, cohesive dough forms, about 5-10 minutes. If the dough is still too sticky, add 1 tablespoon of flour at a time to achieve the correct texture.
If kneading by hand, turn the dough onto a floured surface and knead for about 10 minutes.
Spray a large, clean bowl with oil. Turn the dough into the bowl to coat both sides. Cover and let rise in a warm, draft-free area until doubled, about 45-60 minutes.
Preheat oven to 425 degrees. Line two large baking sheets with parchment.
Punch down the dough and divide into 8 equal balls. Roll each ball into a rope about 2 feet in length. Wrap the right length of the rope towards the center, then twist the left overtop. Wrap the right under the left again to make two little knot things. That's a shit description so hopefully the photos will help. Pinch the two ends to the bottom of the pretzel and set on the baking sheet. Repeat with each ball. Cover and let rise another 15 minutes until slightly puffed.
Bring 6 cups of water to a boil in a large pot. Carefully stir in the baking soda. Drop up to 2 bagels in at a time and boil for 30 seconds. They will deflate. Remove to the baking sheet with a slotted spoon. Repeat with the remaining pretzels.
Blot any extra moisture off the parchment paper and the pretzels with a paper towel. Brush each pretzel with the beaten egg. Sprinkle generously with coarse salt. Bake 12-15 minutes until puffy, golden, and crisp on top. Let cool 5 minutes on the pans, then transfer to a wire rack. Serve!