Preheat oven to 350°.
Pour boiling water over tea bags in a bowl; steep 5 minutes. Remove and discard tea bags; cool to room temperature.
Lightly spoon flour into dry measuring cups; level with a knife. Combine flour, baking soda, salt, and cinnamon, stirring with a whisk. Place the cream cheese and butter in a large bowl; beat with a mixer at medium speed until well blended (about 3 minutes). Add 1/4 cup granulated sugar and brown sugar; beat until well combined. Beat in brewed tea and vegetable oil. Add flour mixture and buttermilk alternately to sugar mixture, beginning and ending with flour mixture; mix after each addition.
Using clean, dry beaters, beat egg whites with a mixer at high speed until foamy. Add cream of tartar; beat until soft peaks form. Add 1/4 cup granulated sugar, 1 tablespoon at a time, beating until stiff peaks form. Gently stir one-third of egg whites into batter; gently fold in remaining egg whites. Spoon batter into a 9-inch square baking pan coated with cooking spray. Bake at 350° for 35 minutes or until a wooden pick inserted in center comes out clean. Cool in pan on a wire rack. Sprinkle with powdered sugar.