Combine tea, milk, oats, cinnamon, ¼ teaspoon ginger, ¼ teaspoon cardamom, and cloves in a resealable bowl. Stir together and refrigerate overnight. (If you do not want to soak the oats overnight, see the notes for a shortcut!)
In the morning, add banana and oat mixture to food processor or blender and process until smooth and well-combined. Add additional ginger and cardamom and sweetener if desired. (I've found that the amount of spice I add depends on the size of the banana that I'm using--start out with a smaller amount and add more if you need to.)
Notes
Making the oat mixture ahead of time and refrigerating it overnight softens the oats and gives the shake a smoother texture. If you're feeling impatient (or don't mind lots of little bits of oatmeal in your shake), you can make this without that step--put the oats in the food processor or blender first, process until it becomes a fine powder, and then add the rest of the ingredients.
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