In the bowl of a stand mixer whisk together the yeast, sugar and warmed milk. Cover with a clean, damp kitchen towel and let sit for 10 minutes until the mixture is frothy.
Add in 2 cups of the flour and begin to mix on low using the dough hook attachment of your stand mixer. Add another cup of flour, the chai spices, dairy-free butter and the egg and mix on medium speed until the dough starts to form. Add in the final cup + ¼ cup of flour and mix until the dough starts to pull away from the sides of the bowl.
Use a rubber spatula to remove the dough from the bowl onto a floured surface and using floured hands, shape the dough into a ball. Place the dough back into the bowl and cover with a clean, damp towel and set aside in a warm area for 1 hour or until the dough has doubled in size.
Punch down the dough to release the air and turn the dough out onto a floured surface and shape the dough into a ball.
Line a 9 x 13 inch (20cm x 30cm) tray with baking paper and set aside. Cut the dough ball into 4 even pieces, and then cut each piece into 3 so that you have 12 pieces in total. Roll each piece into a ball and place evenly into the pan. Cover again with the kitchen towel and set aside in a warm place for 20 minutes.
Before the second rise is complete, preheat the oven to 180°C. Mix together the additional flour, chai spice and water to make a thick paste. Place the paste into a zip lock bag and snip off the end. Once the buns have finished rising, pipe crosses onto each and place the buns in the oven for 30 minutes, or until browned on top and they make a hollow sound when you tap the top.
About 5 minutes before the baking time is up, make the glaze by boiling together the sugar and water in a small pot on the stove until the sugar is completely dissolved. Brush the glaze over the cooked buns. Pull apart and serve warm with some butter.