Blueberry Banana Cake with Cream Cheese Frosting

9x13-inch cake, serves 10 to 12
170g cup unsalted butter, softened
1 cup white sugar
1 cup brown sugar
3 eggs
1 teaspoon vanilla extract
2 tablespoons rum (optional)
1 1/2 cups mashed bananas (from about 3 bananas)
3 cups flour
1 1/2 teaspoons baking soda
1/2 teaspoon salt
1 lemon, juiced and zested
1 1/2 cups milk
2 cups blueberries, washed and picked over
For the cream cheese icing:
20g butter, softened
80g light cream cheese, softened
1 teaspoon finely grated lemon rind
1 1/2 cups icing sugar mixture, sifted

Preheat the oven to 160°C. Line a 9x13-inch pan with parchment paper, with enough paper that paper hangs over the two long sides. Grease lightly with baking spray or butter.
In the bowl of a stand mixer (or in a large bowl with a handheld mixer) cream the butter with the sugars. Blend in the eggs one at a time, and whip until creamy. Add the vanilla and rum, if using, as well as the bananas. Mix until creamy.
Add the flour, baking soda and salt. Stir the mixture roughly, but do not combine completely. In a large measuring cup, mix the lemon juice with the milk. (Reserve the lemon zest for the icing.) With the mixer running, slowly pour the milk into the bowl with the rest of the ingredients. Mix until smooth. Fold in the blueberries. Spread the batter in the prepared pan.
Bake the cake for 75 minutes, or until a tester comes out clean. (Start checking after 60 minutes.) When the cake is firm and a tester comes out clean, remove the cake from the oven. Run a knife between the cake and the short edges of the pan to help release the cake. Lift up on the parchment paper to remove the whole cake from the pan, and place the cake, parchment and all, on a cooling rack. Place the rack in the freezer for 30 minutes. Remove from freezer and let the cake cool completely before icing.
For the icing: Using an electric mixer, beat butter, cream cheese and lemon rind until smooth. Gradually beat in icing sugar until mixture is light and fluffy. Spread icing over cake. Serve.