Preheat the oven to 325 and line 2 baking sheets with parchment paper
Brown the butter in a medium stainless or other light colored skillet over medium heat, It will melt then foam. Continue to stir until you see little brown bits on the bottom of the skillet. Remove from the heat, transfer to a bowl. Place the bowl in the fridge and let it cool for about 20-30 minutes until it’s like soft butter
Sift together the flour, cinnamon, ginger baking soda, and salt into a medium mixing bowl. In a mixer with a paddle attachment, combine the brown butter and sugars on medium high speed for 2-3 minutes
Reduce the speed to low and mix in the milk, eggs and vanilla bean paste. Add in the carrots, and slowly add the flour mixture until just combined. Fold in the pecans and diced candied ginger by hand. Try not to over mix. Scoop the dough with a 2 oz scoop (or ¼ cup) onto the prepared baking sheet
Place about 6 cookies per tray and bake in the oven for 18-22 minutes, they will puff and brown slightly. Remove from the oven and let cool on the baking sheet for about 8-10 min, then move to a cooling rack. Repeat with remaining dough. Let cookies cool completely before frosting
Place the cream cheese, butter, maple syrup, bourbon and vanilla bean paste in the bowl of a stand mixer fitted with the paddle and mix until well combined. Add the powdered sugar and continue to mix, scraping down the sides, as needed. Add more or less powdered sugar to achieve desired consistency. Sandwich two cookies together with frosting for a total of 15 cookie sandwiches