In a food processor, combine all the dry ingredients and pulse until well blended. Set aside. Note: I recommend using a food processor to help blend up the tea into small granular pieces. However, if you do not have a food processor, finely mince the black tea before whisking together in a large bowl.
In a stand-up mixer with the paddle attachment, beat the non-dairy butter, sugar, and vanilla until light and fluffy. Add the pumpkin puree and beat to combine, scraping down the sides of the bowl as necessary. It will look curdled at this point which is fine. It will come back together when the flour is added.
Add the flour mixture in two batches, scraping down the sides in between. Mix until it comes together. Do not over-mix. Once you have a uniform dough, wrap the dough in plastic wrap and chill for at least 1 hour.
Preheat the oven to 375F. Line 2 baking sheets with parchment paper and set aside. Roll dough into balls about 1 tablespoon big, toss in cinnamon sugar. Place on the baking sheet and bake for 8-10 minutes. They should look slightly underdone but will continue to harden as they cool. Let the cookies cool for 5 minutes on the baking sheets before transferring them to a wire cooling rack to cool completely.