Preheat the oven to 350°F (175°C). Line a 9-by-5-inch loaf pan with parchment paper, leaving enough paper extending over the sides to serve as handles when removing the baked loaf.
Place the pumpkin purée, rolled oats, egg whites, maple syrup, cinnamon, nutmeg, baking soda, and vanilla extract in a food processor.
Process the mixture on high speed until the oats are finely broken down and the batter becomes smooth and evenly blended. Pause once during processing to scrape down the sides of the bowl, then continue blending until no visible lumps remain.
Transfer the prepared batter to the lined loaf pan. Use a spatula to spread it evenly and level the surface.
Bake for 30–35 minutes, beginning to test the loaf at the 30-minute mark. The bread is ready when a toothpick inserted into the center comes out clean.
Remove the pan from the oven and allow the bread to cool at room temperature for at least 1 hour.
Use the parchment-paper overhang to lift the cooled loaf from the pan. Cut it into 10 evenly sized slices before serving.