In a large bowl, combine the old-fashioned rolled oats, pumpkin pie spice, chopped pecans, and pumpkin seeds. Stir until evenly combined.
Add the butter to a small saucepan over medium heat. Allow it to melt, then continue cooking, stirring or swirling the pan frequently, as the butter begins to foam. Keep cooking until the milk solids turn golden brown and the butter smells rich and nutty, about 3–5 minutes. Watch it closely, as it can go from browned to burnt quickly.
Remove the browned butter from the heat and stir in the maple syrup, vanilla bean paste, and pumpkin puree. Mix until smooth and well combined.
Pour the warm pumpkin-butter mixture over the dry ingredients. Stir thoroughly until the oats, nuts, and seeds are evenly coated. Spread the granola mixture onto a parchment-lined baking sheet, pressing and spreading it into an even layer.
Bake at 325°F for 35 minutes, flipping and gently stirring the granola halfway through baking.
he granola will still look somewhat wet and soft when it comes out of the oven—don't worry! Allow it to cool completely on the baking sheet. As it cools, the granola will dry out and become crisp and crunchy.