Preheat oven to 350°F (175°C). Grease and flour two 8-inch round cake pans.

In a large bowl, whisk together flour, sugar, baking powder, and salt.

In a separate bowl, combine milk, eggs, vanilla, and softened butter. Gradually add wet ingredients to dry ingredients, mixing until just combined.

Divide batter evenly between the prepared pans and bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean. Let cool in pans for 10 minutes before inverting onto a wire rack to cool completely.

In a saucepan, whisk egg yolks, sugar, and cornstarch until smooth. Gradually whisk in milk.

Cook over medium heat, stirring constantly, until the mixture thickens and boils. Remove from heat and stir in vanilla extract and cold butter until melted and smooth.

Transfer custard to a bowl, cover with plastic wrap directly on the surface to prevent a skin from forming, and chill completely in the refrigerator.

In a cold bowl with cold beaters, whip heavy cream, powdered sugar, and vanilla extract on high speed until stiff peaks form.

Once cake layers and custard are completely cooled, place one cake layer on a serving plate. Spread the chilled custard evenly over the first layer.

Top with the second cake layer. Frost the entire cake with the whipped cream, then chill for at least 1 hour before serving.