Pour the half and half into a microwave safe mug and heat in microwave for 45 seconds.
Remove the mug from the microwave and place the tea bag in the mug to steep.
Mix butter for one minute with electric mixer on medium speed. Add powdered sugar, cinnamon, ginger, cardamom, cloves and vanilla extract. Mix at low speed. After powdered sugar is incorporated into the butter, increase speed to medium and add the tea infused half and half.
Add additional powder sugar if frosting needs a stiffer consistency.
Use immediately or store in a sealed container in the refrigerator up to one month.