Position a rack in the middle of the oven. Preheat the oven to 325°F Line two baking sheets with parchment paper and butter the paper.
Stir the flour, baking powder, baking soda, salt, and cinnamon together in a medium bowl, and set aside. In a large bowl, using an electric mixer on medium speed, beat the eggs and sugar until smooth and lightened in color, about 1 minute. Stop the mixer and scrape the sides of the bowl as needed during mixing. On low speed, mix in the oil, pumpkin, and vanilla until blended. Mix in the flour mixture to incorporate it. Mix in the butterscotch chips.
Using an ice cream scoop with a 1/4-cup capacity, scoop mounds of the dough onto the prepared baking sheets, spacing the cookies at least 2 1/2 inches apart. Or use a measuring cup with a 1/4-cup capacity to scoop out the mounds of dough, then use a thin metal spatula to smooth the mounds.
Bake the cookies one sheet at a time until the tops feel firm and a toothpick inserted in the center comes out dry, about 16 minutes. Cool them on the baking sheets for 5 minutes, then use a wide metal spatula to transfer the cookies to a wire rack to cool completely.
Dust the cooled cookies lightly with powdered sugar. The cookies can be stored in a tightly covered container at room temperature for up to 4 days.