Prior to starting, set the oven's temperature to 350 degrees Fahrenheit. Ensure the 24-cup mini muffin pan is prepared by greasing it thoroughly with a non-stick spray.

Into a medium-sized mixing bowl, sift the flour. Subsequently, incorporate the baking powder, salt, nutmeg, and pumpkin pie spice into the sifted flour.

In a separate, larger mixing bowl, integrate the pumpkin puree and brown sugar.

To this mixture, add the vegetable oil, vanilla extract, and one egg. Incorporate the milk and ensure the mixture is homogenous.

Gradually blend the dry ingredients with the wet mixture, taking care to not overmix to maintain the desired consistency.

Transfer the resulting batter into the pre-prepared mini muffin pan. Each cup should be filled to approximately ¾ of its capacity. Place the pan in the preheated oven and allow the donuts to bake for a duration of 10-12 minutes. The baking is deemed complete when a toothpick, upon insertion, emerges clean.

Upon completion of the baking process, extract the donuts and allow them a brief cooling period, just sufficient to handle.

Prepare two separate bowls; one containing the previously melted butter and another combining the granulated sugar and cinnamon.

Each donut should first be dipped into the melted butter and subsequently coated thoroughly in the cinnamon sugar mixture.

The Baked Pumpkin Donut Holes are best served warm.