Preheat your oven to 350°F (175°C). Lightly grease a 9×5 inch loaf pan with butter or non-stick cooking spray. For even easier removal, you can line the pan with a strip of parchment paper, leaving an overhang on the sides.
In a medium-sized mixing bowl, whisk together the all-purpose flour, baking soda, baking powder, salt, and pumpkin pie spice. Ensure there are no large clumps of spice so the flavor is evenly distributed.
In a separate large bowl, whisk together the pumpkin puree, packed brown sugar, granulated sugar, vegetable oil, eggs, and vanilla extract. Whisk vigorously until the mixture is smooth and the sugars have begun to dissolve into the liquid.
Gradually pour the dry flour mixture into the wet ingredients. Use a spatula or a large spoon to stir the ingredients together until just combined. Be careful not to overmix, as this can make the bread tough; stop as soon as you see no more streaks of white flour.
Pour the batter into the prepared loaf pan and smooth the top with a spatula. Place the pan in the center of the oven and bake for 50 to 60 minutes. The bread is done when a toothpick inserted into the center comes out clean or with just a few moist crumbs.
Remove the pan from the oven and let the bread cool in the pan for about 10 minutes. Then, carefully transfer the loaf to a wire rack to cool completely before slicing. This helps the structure set and makes it easier to cut clean slices.