Preheat the oven to 350°F. Place paper liners in a muffin tin, then lightly coat the inside of each liner with the avocado oil to help prevent the baked muffins from sticking.
Allow the eggs, butter, and cream cheese to come to room temperature while the oven heats. Place the coconut flour through a sifter into a small bowl so that any compacted pieces are removed before mixing.
In a large bowl, whisk together the room-temperature eggs, ½ cup pumpkin puree, melted and cooled butter, 1 teaspoon stevia glycerite, 2 teaspoons vanilla extract, and 2 teaspoons cinnamon.
Continue whisking for approximately 1–2 minutes, until the mixture is thoroughly blended and becomes slightly lighter in appearance.
Using a spatula, gently fold the sifted coconut flour and gluten-free baking powder into the wet mixture. Mix only until evenly incorporated, taking care not to overwork the batter.
Distribute the prepared batter evenly among the lined muffin cups, filling each one roughly three-quarters of the way to leave sufficient space for the muffins to rise.
Bake at 350°F for 22–25 minutes. The muffins are ready when their tops appear set and lightly golden and a toothpick inserted into the center comes out clean or with only a few moist crumbs attached.
Remove the muffin tin from the oven and leave the muffins in the pan for 5 minutes so they can firm sufficiently before being moved.
Meanwhile, place the softened cream cheese, ¼ cup pumpkin puree, 1 teaspoon stevia glycerite, ½ teaspoon cinnamon, and ½ teaspoon vanilla extract in a clean mixing bowl. Beat for 1–2 minutes, or until the frosting is uniformly smooth, creamy, and free of lumps.
After the muffins have rested for 5 minutes, transfer them to a wire cooling rack. Allow them to cool completely before applying the frosting so the cream cheese mixture does not soften or melt.
Once completely cooled, generously spread or pipe the prepared pumpkin cream cheese frosting over the top of each muffin.