Preheat oven to 375°F (190°C). Grease two 12-donut baking molds.
In small bowl, whisk together flour, baking powder, pumpkin pie spice and salt.
In medium bowl, whisk together egg, pumpkin, brown sugar, milk, vegetable oil and vanilla until well blended. Stir in flour mixture just until incorporated. Divide batter evenly among donut molds.
Bake for 12 to 15 minutes or until deep golden brown. Let cool in molds for 2 minutes, or until cool enough to handle.
Meanwhile, in small microwave-safe bowl, melt butter.
In shallow bowl, stir together granulated sugar and cinnamon. Toss warm donut bites in butter, then cinnamon sugar to coat.