Preheat the oven to 350 F, and spray the bottoms of three 8-inch cake pans with non-stick baking spray.
Warm the milk until very hot, almost boiling, then remove from the heat. Add the tea bags, let steep for 10 minutes, then throw away the tea bags.
Meanwhile, in a large bowl, sift together the flour, sugar, baking powder, salt and spices, then whisk until well combined.
In a separate bowl, whisk together the eggs, egg whites, buttermilk, melted butter, oil and vanilla, and whisk until smooth. Whisk in the warm chai tea milk.
Add the dry ingredients to the wet, and whisk until combined and smooth, about 10-15 seconds. Divide the batter between the cake pans. Tap a few times against the counter to pop any large air bubbles.
Bake the cakes for about 21-25 minutes, or until a cake tester or a toothpick comes out clean, and the tops spring back when lightly touched.
Set the pans on a cooling rack, cover them loosely with a clean kitchen towel, and cool completely before frosting. When ready to frost and assemble the cake, remove the cakes from the pans.