Preheat your oven to 350°F. Line your baking sheets with parchment paper and set them aside.

In a medium bowl, mix together the flour, baking soda, baking powder, ground cinnamon, ground nutmeg, and salt.

In a separate large bowl, cream the softened butter and sugar until light and fluffy.

Blend in the pumpkin puree, egg, and vanilla extract until smooth.

Gradually incorporate the flour mixture into the pumpkin mixture, stirring gently to combine.

Drop rounded tablespoons of cookie dough onto prepared baking sheets with space between them.

Bake the cookies for 15-18 minutes until the edges feel firm and the cookies are golden.

Allow the cookies to cool on the baking sheet for a few minutes before transferring to wire racks to cool completely.

Melt one stick of butter in a small saucepan over medium-low heat until it turns golden brown.

Remove the browned butter from heat and let it cool completely.

Beat the remaining butter until smooth; mix in the cooled browned butter.

Add the brown sugar, pumpkin puree, ground cinnamon, and ground nutmeg, stirring well.

Gradually add powdered sugar to achieve a smooth frosting texture.

Once the cookies are completely cooled, frost them with the caramel frosting.

Store any leftover cookies in an airtight container.