1. 1. Combine Wet Ingredients: In a large mixing bowl, whisk together the active sourdough starter, pumpkin puree, granulated sugar, egg, melted butter, and vanilla extract until well combined and smooth. The mixture should have a light orange hue and a creamy consistency.

2. 2. Mix Dry Ingredients: In a separate medium bowl, whisk together the all-purpose flour, baking powder, baking soda, ground cinnamon, ground nutmeg, ground ginger, and salt. Ensure all dry ingredients are evenly distributed to prevent lumps in the final dough.

3. 3. Form the Dough: Gradually add the dry ingredients to the wet ingredients, mixing with a spatula or wooden spoon until just combined. Be careful not to overmix; a few streaks of flour are fine. The dough will be soft and slightly sticky.

4. 4. Prepare for Frying: Lightly flour a clean surface. Turn the dough out onto the floured surface and gently pat or roll it out to about 1/2-inch thickness. Use a donut cutter or two different-sized round cutters (one for the donut, one for the hole) to cut out your donuts. Gather and re-roll scraps as needed.

5. 5. Heat the Oil: Pour vegetable oil into a large heavy-bottomed pot or Dutch oven to a depth of about 2-3 inches. Heat the oil over medium heat until it reaches 350 F (175 C). Use a candy thermometer to monitor the temperature for best results.

6. 6. Fry the Donuts: Carefully place 2-3 donuts into the hot oil, being careful not to overcrowd the pot. Fry for 1-2 minutes per side, or until golden brown and cooked through. The donuts will puff up and develop a beautiful crisp exterior.

7. 7. Drain and Dust: Using a slotted spoon or spider, remove the fried donuts from the oil and place them on a wire rack lined with paper towels to drain excess oil. While still warm, dust generously with powdered sugar.

8. 8. Serve Warm: Serve your homemade sourdough pumpkin donuts warm for the best flavor and texture.