Measure 4 5.75x8 inch rectangles on parchment paper and cut them to size. Set aside.
In a medium saucepan, heat butter, brown sugar, salt, pumpkin puree and water together over medium-high heat until it boils. Immediately add all of the flour, 1 teaspoon of cinnamon, all the ginger, cloves, and nutmeg and stir with a wooden spoon. Continue to stir over heat until a dough forms. Remove from heat and transfer dough to a medium bowl to cool down for 3 minutes.
Once slightly cooled, add 1 egg to dough and stir vigorously until combined into dough. Repeat with rest of eggs, one at a time. In a large Dutch oven, heat about 3 inches of oil over medium heat. Add a candy thermometer to monitor the oil temperature. Once the oil reaches 375°F, it’s ready for frying.
Transfer mixture to a large pastry bag fitted with a large star piping tip. Spread out all 4 rectangles of parchment paper. Slowly pipe 4 strips of dough onto each rectangle, making sure to keep the strips about 1 inch away from eachother. Repeat on all rectangles of parchment.
Slowly place one rectangle with piped dough into hot oil. Place another right next to it. Do not add more than 1 at a time. Let the dough cook with the parchment for 30 seconds or until you can gently slide off the parchment. Discard parchment paper. Keep cooking for 2 minutes, flip, and cook for 2 minutes longer. Monitor the oil temperature to ensure it doesn’t go lower than 350°F or higher than 385°F. Remove the cooked churros and drain them on a plate lined with paper towels. Repeat the process until all the dough has been fried.
Place the sugar to a shallow bowl and mix with remaining 2 teaspoons of cinnamon. Toss the churros to coat in the cinnamon sugar, no more than 2 at a time. Serve warm.