Preheat oven to 350°F with rack in middle. Line 2 large baking sheets with parchment paper.
Whisk together flour, baking powder, soda, salt, and spices in a bowl.
Whisk together sugar, oil, pumpkin, egg, and vanilla in a separate large bowl until well combined, then stir in flour mixture.
Using a 1-ounce ice cream scoop or tablespoon measure, drop a scant scoop's worth of batter or 2 scant tablespoons of batter onto a lined baking sheet to form 1 mound. Make 15 more mounds, arranging them 2 inches apart until baking sheet is full (you will have batter left over).
Bake until springy to the touch, 12 to 18 minutes. Transfer cookie-cakes to rack to cool.
Form and bake remaining batter on the other parchment-lined sheet. You should have a total of 32 cookie-cakes.