Preheat oven to 375 degrees F. Line 2 cookie sheets with parchment paper.
In a large bowl, whisk together flour, 1-2 tsp chai spice, baking soda, baking powder and salt. (*note: chai spices will be used in filling also, so adapt amount in cookie to your preference of chai flavor)
In a small saucepan, add the unsalted butter and let simmer over med-low heat 5-8 minutes, stirring occasionally. Use sensory clues to tell when it is done. It should be amber brown in color and give off a nutty scent. It will foam, but should not be boiling hard. Take off the heat and let cool.
In mixer, beat sugars and eggs together to combine. Slowly add brown butter and beat together briefly to combine. Add pumpkin and buttermilk and beat all together until light and creamy.
In small bowl combine milk, baking soda and vinegar and stir thoroughly.
Add half of the flour mixture to the pumpkin mixture still in the mixer, then add the milk-vinegar mixture, and then add the rest of the flour mixture. Beat all of it together slowly, only until combined. Do not over mix.
Drop about 1-2 Tbsp of batter onto the baking sheets. Use 2"-diameter ice cream scoop for large whoopies (flatten them with back of the scoop). Cookies will spread, so give them ample room on the cookie sheet. If desired, add chopped nuts to 1/2 of the cookies (these will be the tops)
Bake 8-10 minutes or until cookies just start to brown. Slide parchment and cookies onto cooling rack, and let them cool completely before putting them together with filling.