Preheat the oven to 350 degrees F and line a large baking sheet with parchment paper.
Add butter to a saucepan over medium heat. Melt then cook for 6-8 minutes while stirring often. The butter begin to foam and turn golden brown. Once the foam reduces and you see brown milk solids at the bottom, pour into a large mixing bowl.
Cool the browned butter for about 10 minutes, then add in brown sugar, granulated sugar, egg yolk, and vanilla extract. Whisk until smooth.
Add pumpkin puree and whisk to combine.
In a separate bowl, stir together gluten free flour, pumpkin pie spice, baking soda and sea salt until combined.
Add dry ingredients to wet ingredients and stir until just combined.
Scoop dough by rounded tablespoons and roll into balls. Place them on the parchment lined baking sheet and use your hands to flatten slightly. Make sure they are about 2 inches apart.
Bake for 10-12 minutes until the edges are the golden and the centers are puffed up. Cool for 10 minutes then transfer to a wire rack to cool completely.
Make the cream cheese frosting: Add cream cheese, butter, and vanilla extract to a bowl, and use an electric mixer to beat until smooth. Slowly add in powdered sugar until smooth and spreadable. You can add a bit more water if you want a thinner consistency for drizzling.
Frost or drizzle the cookies with the frosting. You can sprinkle the top with cinnamon or pumpkin pie spice, if you want.