For cake: Preheat oven to 350 degrees. Sift together flour, baking soda, baking powder, and salt and set aside. Combine butter and sugar, beating until almost white. Add eggs, 1 at a time, then bananas. Stir in yogurt and vanilla. Fold in combined dry ingredients a little at a time until completely incorporated and mixture is smooth. Pour into buttered and floured 8-inch cake tin and bake for 40 minutes. Turn onto wire rack to cool. Regrease cake tin with butter only and set aside.
For filling: Beat together sugar and butter until almost white. Add eggs, 1 at a time, beating thoroughly before each addition. Mix together cocoa and coffee. Then add Tia Maria to coffee/cocoa mixture and add all to filling.
Cut cake into 2 layers, horizontally, and place 1 layer in bottom of greased cake pan. Cover with half of filling and then the remaining layer of cake. Top with remaining filling. To rid cake of air holes, hold it 12 inches from table and drop it so it lands flat. Repeat this twice. Cover cake with plastic wrap and freeze for 2 hours. Serve ice cold with vanilla ice cream.
*RAW EGG WARNING
Food Network Kitchens suggest caution in consuming raw and lightly-cooked eggs due to the slight risk of Salmonella or other food-borne illness. To reduce this risk, we recommend you use only fresh, properly-refrigerated, clean, grade A or AA eggs with intact shells, and avoid contact between the yolks or whites and the shell.