Preheat doughnut maker (or your oven to 350) and if using a doughnut pan, grease with cooking spray. Combine sugar with spices (cinnamon through nutmeg) until well mixed. Remove 3/4 cup sugar for the actual doughnut batter, set aside the remaining 1 1/2 cups for later. Meanwhile, in a measuring cup combine milk and vinegar and let stand 5 minutes.
In a large bowl combine the 3/4 cup sugar/spice mixture with flour, baking powder, and salt. Open chai tea bag and stir contents into the flour mixture. In a separate, smaller bowl, whisk together milk/vinegar mixture with melted butter, egg, and vanilla.
Pour wet ingredient mixture over dry ingredient mixture and stir with wooden spoon until just combined and the batter looks smooth.
Spray doughnut maker with cooking spray and fill cavities 1/2 full with doughnut batter; if using the oven fill doughnut pan cavities halfway full with batter.
Bake for 4 minutes, or until doughnuts spring back when lightly touched or a toothpick comes out clean.
Place remaining sugar/spice mixture from step one in a plastic or paper bag and have your 6 tbsp melted butter in a small bowl.
Working two or so at a time, dip doughnuts in melted butter, then place in bag with sugar mixture. Gently toss/shake the bag to cover the doughnuts. Remove and set on piece of parchment paper while you dip the rest of the doughnuts.