Preheat your oven to 350°F (175°C).

In a large bowl, beat together ½ cup softened butter and ¾ cup granulated sugar until creamy—about 3-5 minutes.

Add 2 large eggs, 1 teaspoon vanilla extract and mix.

Gradually stir in 1 ½ cups all-purpose flour, 1 teaspoon baking powder, ½ teaspoon baking soda, and ¼ teaspoon salt, alternating with ½ cup buttermilk until smooth.

Pour the batter into a greased 9x13 inch baking pan.

Bake for 25-30 minutes, or until a toothpick comes out clean.

Cool completely in the pan on a wire rack.

In a saucepan, combine 2 cups whole milk, ½ cup sugar, ¼ cup cornstarch, and 4 large egg yolks.

Cook over medium heat, whisking constantly, until thickened (around 7-10 minutes).

Remove from heat and add 2 tablespoons of butter and 1 tablespoon vanilla extract; stir until smooth.

Slice the cooled cake into two even layers.

Layer half of the pudding on the bottom layer, followed by banana slices.

Add top layer and repeat with remaining pudding and bananas.

Top with whipped cream or meringue if desired.

Garnish with crushed vanilla wafers or graham crackers.

Chill for at least 30 minutes before serving.

Slice into squares and serve.