Preheat your oven to 350°F (175°C).
In a large mixing bowl, cream together the softened butter, brown sugar, and granulated sugar until light and fluffy.
Add in the pumpkin puree, eggs, and vanilla extract, mixing until well combined.
In a separate bowl, whisk together the flour, baking soda, baking powder, cinnamon, nutmeg, and salt.
Gradually add the dry ingredients to the wet mixture, stirring until just combined.
Drop spoonfuls of dough onto a lined baking sheet, spacing them about 2 inches apart.
Bake in the preheated oven for 12-15 minutes, or until the edges are lightly golden.
Remove from the oven and let cool on the baking sheet for about 5 minutes before transferring to wire racks to cool completely.
Once the cookies are cool, take one cookie, place a scoop of vanilla ice cream on the flat side, and top with another cookie. Press gently to form a sandwich.
Repeat with remaining cookies and ice cream.