Cream together sugar and the butter until light and fluffy. Beat in the egg and vanilla. In a separate bowl, sift together flour, baking powder, salt, and spices. Alternate adding the flour mixture and the milk, beating well after each addition.
Fill lined cupcake tins 2/3 full. Bake at 350 for 18-20 minutes, or until test done with toothpick. Remove from the tins immediately and cool on a wire rack.
Frosting
Heat milk until it simmers. Remove from heat, then add the tea bag and steep for 5 minutes.
Using a stand mixer with paddle attachment, mix together butter, salt, and extract until well blended. Add spices. Gradually add powdered sugar one cup at a time and whip vigorously. Gradually add tea-infused milk until desired consistency is reached.