Preheat your oven to 350°F (180°C). Bake the pumpkin until tender. Then, puree with an immersion blender or fork.
In a large bowl, whisk together the flour, sugar, salt, baking powder, cinnamon, and nutmeg.
In another bowl, whisk the eggs, then add the pumpkin puree, milk, and melted butter.
Combine the dry and wet ingredients, and mix well to form a dough.
Heat the oil in a deep fryer or large pot to 340-355°F (170-180°C).
Drop small spoonfuls of dough into the hot oil and fry until golden brown, about 3-4 minutes, turning occasionally.
Remove the doughnuts with a slotted spoon and place them on a paper towel-lined plate to drain excess oil.
Dust the doughnuts with powdered sugar and serve fresh.
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