For cake layers, preheat oven to 350 °F and grease cake pans and line bottoms and sides with parchment paper.
For cake, cream butter and sugar together until light and fluffy. Beat in eggs one at a time and stir in vanilla extract. Stir in bananas. In a separate bowl, sift together flour, baking powder, baking soda, cardamom and salt and stir into banana mixture. Spoon batter into prepared pans and spread evenly, checking that batter comes up to the same height in both pans. Bake for 30 minutes for 6-inch cake, about 50 minutes for the 12-inch, until a tester inserted in the center of the cakes comes out clean. Allow to cool 10 minutes in the pans, then turn out onto a cooling rack to cool completely.
For buttercream, whip egg whites with cream of tartar until foamy and add 1 cup of sugar, whipping until whites hold a soft peak. In a saucepot, combine remaining 1 ½ cups sugar and bring up to a boil. Using a candy thermometer, boil sugar without stirring until the temperature reaches 240 °F (or if you don’t have a candy thermometer, spoon a little hot sugar into a cup of cool water – when the sugar makes a “soft ball” then it’s ready).
Remove from heat and carefully pour sugar slowly down the side of the egg white bowl, whipping on medium speed. Continue whipping until all sugar has been added and keep whipping until whites have cooled to room temperature, about 5 minutes. Still beating, add butter a little at a time until all has been added. The egg whites will deflate, but the butter adds back volume. Beat buttercream until smooth and stir in vanilla extract. Store buttercream at room temperature if frosting cake the same day, or refrigerate then bring up to room temperature and beat again to return to spreadable texture.
To assemble cake, slice 12-inch cake across into 2 layers. Place bottom layer onto large cake platter. Spread a thin, ¼ -inch layer of butterceam onto cake and top with top layer of cake. Repeat process with 6-inch cake. You may find it easier to place the 6-inch tier on a flat plate or cookie sheet to get to the lower edge most effectively.
To frost cake, spread a ¼ -inch layer of buttercream over top of 12-inch cake layer pushing frosting over the sides of the cake with an offset spatula. Spread frosting on side of the cake, connecting frosting with overhanging edges to create clean lines and corners. Run your spatula around cake to smooth buttercream. For an even smoother effect, dip your spatula in boiling hot water, wipe to dry and smooth buttercream. Chill cake while preparing other tiers. Keep remaining frosting handy for touch-ups.
To make sure layers remain stable, they must rest on wooden doweling. To do this, insert a length of doweling into bottom tier, at least 4 inches from the outside edge. Mark where the top of the cake ends at the doweling with a pen and remove. Cut doweling to marked length and cut 4 more pieces of identical length (this ensures your cake sits level, even if the frosting is just a hint off). Insert the five pieces of doweling into the cake in a circle and gently place the 6-inch tier on top, checking that tier is centred (or angled if desired). Touch up any dents with your spatula, clean-up edges and chill.
To decorate, arrange whole seasonal fruit on cake, cascading down. Chill cake completely until ready to display.
This wedding cake can sit on display for up to 6 hours in an air-conditioned room, 1 ½ hours outside (out of direct sunlight). The cake cuts easier if it is chilled for 20 minutes before slicing, but will still cut well otherwise.