1. Center a rack in oven and heat oven to 350 degrees F. Line an 8" square baking pan with a long piece of foil, letting excess hang over sides of pan to form a sling; coat with cooking spray and set aside.
2. In a large bowl, whisk brown sugar, pumpkin, oil, egg whites, vanilla, pumpkin pie spice, and salt. Using a rubber spatula, stir in oats until moistened, then mix in remaining ingredients. Transfer to prepared pan and spread into an even layer, then use hands to press firmly until mixture is very flat.
3. Transfer to oven and bake until top is golden brown, about 40 minutes (do not turn oven off). Cool 15 minutes in pan, then invert onto a cutting board and cut into 12 even rectangles. Line a baking sheet with a fresh piece of foil and arrange bars on top, keeping the bars inverted as they were on the cutting board so second side faces up. Bake until deeply golden brown, about 15 minutes.
4. Cool completely, about 15 minutes, then store in an airtight container at room temperature for up to 3 days.