Preheat the oven to 190ºC (170ºC fan). Grease a doughnut pan with cooking spray.
In a small pot, heat the milk over medium high and heat until simmering. Remove from the heat and submerge the chai teabags in the milk. Allow to infuse for 5 minutes.
Remove the teabags, using the back of a spoon to squeeze out all the milk that may have been absorbed by them.
Meanwhile, whisk together flour, granulated sugar, baking powder, cinnamon, and allspice in a large bowl. Add the egg, vegetable oil, 3 tablespoons of the chai infused milk, yogurt, and vanilla. Refrigerate the remaining chai milk until you are ready to make the glaze. Stir the batter until all the dry ingredients are incorporated.
Transfer the batter to a large zip top bag and snip off one of the corners. Squeeze the batter evenly into the doughnut pan. Alternatively, you could use a couple of spoons to spoon the batter into the pan.
Bake for 10-12 minutes until donuts are springy and lightly browned.
Remove from the oven and allow to cool for 5 minutes before turning out onto a cooling rack to cool completely.
Once the doughnuts are cool, prepare the glaze by adding the icing sugar to a small bowl along with 2 teaspoons vanilla extract and about 1 tablespoon of the chai infused milk. Stir until smooth and shiny, adding a few drops of chai milk at a time until the desired consistency is reached.
Dip one side of the doughnuts in the glaze and return to the cooling rack to let it set. Sprinkle with additional cinnamon if desired.
Serve and enjoy!