To make the cake:
Preheat oven to 350°F and grease a 9x13-inch baking pan.
With an electric mixer, beat the butter and sugar on high speed until pale and creamy, about 3-4 minutes. Scrape down the bowl as needed.
Add the eggs one at a time, mixing and scraping the bowl down after each addition. Add vanilla.
Add the flour, baking powder and salt and mix until just combined. Batter will be very thick.
Spread batter into prepared pan and bake until edges turn golden and pull away from the pan and the center bounces back when gently pressed, 35-40 minutes.
Let cool completely, about 60 minutes, then poke holes all over with a fork or skewer.
To make the milk filling:
In a large bowl, whisk together the whole milk, evaporated milk and sweetened condensed milk.
Pour over the cooled cake. Mixture will completely cover cake.
Chill in the fridge until almost all of the milk filling has absorbed into the cake, about 3-4 hours.
To frost the cake:
With an electric mixer, beat the heavy whipping cream, vanilla and sugar until thickened to medium peaks.
Spread over cake and chill until ready to serve. The cake will keep in the fridge for several days.
Calories: 450kcal, Carbohydrates: 53g, Protein: 10g, Fat: 23g, Saturated Fat: 14g, Cholesterol: 137mg, Sodium: 213mg, Potassium: 326mg, Fiber: 1g, Sugar: 41g, Vitamin A: 816IU, Vitamin C: 2mg, Calcium: 233mg, Iron: 1mg