In a bowl attached to a stand mixer, cream together coconut oil and brown sugar until light and creamy, several minutes. Add in pumpkin and beat together for another minute.
In a medium-sized bowl measure out dry ingredients: flour, baking powder & soda, cinnamon, and salt, whisking to combine.
With mixer on low speed, gradually add in dry ingredients to the wet ingredients, mixing until just combined.
Using a medium cookie scoop, scoop out dough onto cookie sheets, spaced about 2″ apart. Bake for 8-10 minutes until tops feel done (or just slightly underbaked) when touched. Let cool on sheet for 10 minutes before transferring to a wire rack to cool completely.
Brown the butter: Take 1/4 cup (4 Tbsp) of butter and melt it in a saucepan on top of the stove over medium heat. Stir until you see brown bits appear (about 10 minutes) and the butter has a nutty smell to it. Remove from heat and let cool for about 20 minutes.
In a bowl attached to a stand mixer, take remaining 2 Tbsp of butter, brown butter, and cream cheese and mix until light and creamy, several minutes.
With mixer on low speed, gradually add in confectioners’ sugar, vanilla extract, and half and half. Add a little half and half in at a time until you reach your desired creaminess. Beat for 2 more minutes until light and fluffy.
When cookies are completely cooled, spread icing on top. Store in airtight container in refrigerator.