Preheat your oven to 350°F (175°C). Grease and flour two round baking pans.
In a bowl, whisk together flour, baking powder, and salt.
In another bowl, beat butter and sugar until fluffy. Add eggs one at a time, mixing well after each addition. Then fold in mashed bananas and vanilla extract.
Gradually blend in dry ingredients with milk until just combined—do not overmix.
Pour batter into prepared pans and bake for 25-30 minutes until golden brown. Cool completely before assembling.
Layer the first cake with vanilla pudding mixed with milk, top with the second layer, and finish with whipped cream and banana slices.