Measure out 2/3 cup of pumpkin puree and place it onto a paper towel in a bowl to start releasing its liquid while you work on the brown butter. Set aside.
Place a medium saucepan over medium/high heat and add 1/2 cup (1 stick) of unsalted butter cut into 1 Tbsp cubes. Brown the butter by allowing the butter to melt, foam and then produce toasted "brown" bits at the bottom of the pan. The butter should smell nutty at this stage. Keep an eye on the pan as it can go from browned to burnt quickly.
Pour the browned butter into a bowl, remembering to include all of the browned bits left in the pan. Immediately add 1 Tbsp of cold butter to the bowl and stir until it melts.
Add ice to a bowl larger than the bowl with the browned butter. Place the bowl with the browned butter onto the ice and stir until the butter goes from liquid to a solid, spreadable consistency (about 5-7 minutes)
Place the cooled browned butter into a large bowl and add 1/2 cup of granulated sugar, 1/2 cup of dark brown sugar and 1 large egg yolk. Mix until just combined.
Take the bowl with the pumpkin puree (lots of liquid should have released by now) and use either a paper towel or cheese cloth to strain the rest of the liquid. After straining you should have 1/3 cup of pumpkin puree.
Add the strained pumpkin puree (1/3 cup) to the butter sugar mixture and mix until just combined.
In a separate bowl, combine 1 1/2 cups of all purpose flour, 1/2 tsp of baking soda, 1/2 tsp of cream of tartar, 1/2 tsp of cinnamon, 1/2 tsp of salt and 1/4 tsp of nutmeg and mix until combined.
Add the dry mixture to the wet mixture and mix until dough forms.
Scoop out 12 balls of dough and refrigerate for 1 hour. Optional: weigh each ball of dough for even cookies. Each ball should weigh roughly 50g.