In a large bowl, whisk together the pumpkin puree, vegetable oil, eggs, granulated sugar, brown sugar, and vanilla extract until smooth and well combined.
In a separate bowl, whisk together the all-purpose flour, baking soda, baking powder, pumpkin pie spice, ground cinnamon, and salt until evenly mixed.
Gently fold the dry ingredients into the wet ingredients until just combined, then add the sour cream and fold it in. The sour cream is the key to an incredibly moist crumb.
Be careful not to overmix — a few small streaks of flour are perfectly fine.
Grease a 7x3-inch or 8x4-inch loaf pan that fits inside your air fryer and line the bottom with a strip of parchment paper for easy removal. Pour the batter into the prepared pan and smooth the top with a spatula.
Place the loaf pan in the air fryer basket. Air fry at 310°F for 40 to 50 minutes. Check around the 35-minute mark — if the top is browning too quickly, loosely tent a small piece of aluminum foil over it.
The bread is done when a toothpick inserted into the center comes out clean or with just a few moist crumbs.
Carefully remove the pan from the air fryer and let the bread cool in the pan for 10 minutes. Then gently turn it out onto a wire rack and let it cool for at least 20 more minutes before slicing.
Slice and serve warm or at room temperature. This bread is even more flavorful the next day once the spices have had time to fully develop.