In a medium bowl, whisk together the pumpkin puree, softened cream cheese, ground cinnamon, grated nutmeg, salt, vanilla extract, egg, and packed brown sugar until the mixture is smooth and creamy. Set the filling aside while you prepare the dough.
In a large bowl, whisk together the all-purpose flour, cane sugar, and salt. Add the very cold cubed unsalted butter, and quickly rub it into the flour mixture with your hands until it resembles small peas. Sprinkle in 2 tablespoons of ice water and fluff with two forks. Continue adding ice water, one tablespoon at a time, fluffing after each addition, until you’ve incorporated a total of 5 tablespoons. If the dough still looks dry, add more water in 1/2 teaspoon increments until the dough forms shaggy crumbs.
Turn the dough onto a work surface and gently knead just a few times until it comes together. Divide the dough into two pieces, flatten each into a disk, wrap in plastic wrap, and refrigerate for at least 1 hour. When ready, remove one piece of dough from the fridge and let it sit for about 10 minutes. On a generously floured surface, roll out the dough until it's about 1/8 inch thick. Using a 4-inch cutter or glass, cut out 8 dough rounds and return them to the refrigerator. Repeat with the second dough disk to get a total of 16 rounds. I like to refrigerate the cut rounds—this keeps the butter cold and helps the pastry bake up extra flaky.
Place about 2 1/2 teaspoons of the pumpkin and cream cheese filling onto the center of each dough round. Moisten the edges with water, fold each round over the filling to make a half-moon shape, then press to seal. Use a fork to crimp the edges, ensuring they are fully closed to keep the filling from leaking during baking.
Line a baking sheet with parchment paper and arrange the assembled empanadas on it. Freeze the empanadas for 15 minutes to help them hold their shape during baking. While they chill, preheat your oven to 375°F (190°C).
Remove the empanadas from the freezer. In a small bowl, whisk together 1 egg with 1 tablespoon water to make the egg wash. Brush each empanada with the egg wash. In a separate small bowl, mix the cane sugar with ground cinnamon for sprinkling, then sprinkle this mixture generously over the empanadas. For a lovely golden color and sparkle, I always make sure to coat them well with the sweet cinnamon topping.
Bake the empanadas in the preheated oven for about 20 minutes, or until they are puffed and golden brown. Allow them to cool slightly before serving. These empanadas are delicious warm, but I like them just as much at room temperature for a sweet snack later.