Preparation Steps

• Preheat oven to 350°F (175°C). Line baking sheets with parchment paper.
• In a large bowl, cream together softened butter, granulated sugar, and brown sugar until light and fluffy.
• Beat in the egg and vanilla extract.
• In a separate bowl, whisk together flour, baking soda, and salt.
• Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Stir in the rolled oats.
• Drop rounded tablespoons of dough onto the prepared baking sheets, about 2 inches apart.
• Bake for 12-15 minutes, or until golden brown around the edges. Let cool on the baking sheets for a few minutes before transferring to a wire rack to cool completely.
• To make the filling, whisk together milk, granulated sugar, cornstarch, and egg yolks in a medium saucepan.
• Cook over medium heat, stirring constantly, until the mixture thickens and comes to a boil. Boil for 1 minute, stirring continuously.
• Remove from heat and stir in the butter and vanilla extract until smooth.
• Stir in the mashed bananas. Cover the surface of the filling with plastic wrap to prevent a skin from forming and let it cool completely.
• Once the cookie halves and filling are cool, spread a generous amount of filling onto the bottom of one cookie half and top with another cookie half.
• Chill for at least 1 hour before serving.