Preheat convection oven to 350°F (175°C) and line heavy-gauge baking sheets with silicone mats or parchment paper.

In a stand mixer fitted with a paddle attachment, cream 1/2 cup butter and granulated sugar on medium-high speed until the mixture reaches a light, aerated texture.

Incorporate pumpkin puree, egg, and vanilla extract, mixing until a homogenous wet emulsion is formed.

In a separate vessel, whisk together flour, baking powder, baking soda, 1 teaspoon cinnamon, nutmeg, and salt to ensure even leavening distribution.

Reduce mixer speed to low and gradually introduce the dry ingredients into the wet mixture, mixing only until no dry streaks remain to prevent gluten over-development.

Using a #40 scoop, portion the dough into 2-tablespoon spheres onto the prepared sheets, maintaining 2-inch intervals.

Bake for 10 to 12 minutes or until the internal structure is set and the surfaces are matte.

Transfer the cookies to a wire cooling rack and allow to reach an internal temperature of 75°F (24°C) before applying frosting.

Prepare the frosting by whipping the remaining 1/2 cup butter, powdered sugar, 1 teaspoon cinnamon, and heavy cream until a stable, fluffy consistency is achieved.

Apply 1 tablespoon of frosting to the apex of each cooled cookie and spread evenly with an offset spatula.