Preheat the oven to 350°F (175°C). Line an 8×8-inch baking pan with parchment paper, leaving a slight overhang on two sides for easy removal. Lightly grease the parchment.
In a large bowl, whisk together the pumpkin puree, maple syrup, melted coconut oil (or butter), eggs, and vanilla until smooth and fully combined. The mixture should look glossy and uniform.
Stir in the rolled oats, flour, baking powder, pumpkin pie spice, and salt. Mix until no dry pockets remain. The batter will be thick and sticky. Fold in any optional nuts or chips if using.
Transfer the mixture to the prepared pan. Use a spatula or the back of a spoon to press it evenly into the corners. Smooth the top so the bars bake uniformly.
Bake for 28–32 minutes. The edges should look golden and the center should feel set when gently pressed. A toothpick inserted in the middle should come out with a few moist crumbs, not wet batter.
Let the pan cool on a wire rack for at least 30 minutes. Then lift the bars out using the parchment overhang and cool fully before slicing into 12 squares. Cooling helps them firm up for clean cuts.