Preheat oven to 350°F (180°C). Grease and flour two 8-in. (20 cm) round pans. Set aside. In a medium saucepan, heat milk over medium heat, add tea bags, remove from heat and steep, 15 min. Remove and discard tea bags, set milk aside and cool completely.
In a bowl, blend together flour, baking powder and salt. Set aside. Using an electric mixer (stand or hand-held) on medium, blend brown sugar, oil, eggs and vanilla until creamy, about 3 min. Reduce speed to low, alternately add in cooled milk and flour mixture and mix until smooth. Divide batter evenly among pans and bake on middle rack of oven 30 min. or until a toothpick comes out clean. Cool in pans 10 min. then remove to cooling rack to cool completely.
Using mixer on medium, whip egg whites, cream of tartar and vanilla until soft peaks form, about 4 min. Set aside. In a large saucepan, combine sugar and 1 cup (250 mL) water over medium-high heat and bring to a boil, stirring occasionally. Once boiling, cover, reduce heat to medium and cook, without stirring, until mixture thickens and a candy thermometer reads 240°F (116°C), about 4 min. Slowly pour sugar syrup into egg whites and whip until stiff peaks form, about 10 min.
Slice top off each cake to create a flat surface then slice each cake in half horizontally. Place a dollop of icing on centre of serving dish, place 1 cake layer on top and spread an even layer of icing overtop. Repeat for remaining layers. Ice top and sides with remaining icing. Cake will keep covered, at room temperature, for up to 3 days.