Preheat oven to 350°F (175°C). Grease and flour a 9x13 inch baking pan.
Cream together the butter and sugar until light and fluffy. Beat in eggs one at a time, then stir in the vanilla.
In a separate bowl, whisk together the flour, baking powder, and salt. Gradually add to the creamed mixture, alternating with the milk, and mix until just combined.
Pour batter into the prepared pan and bake for 30-35 minutes, or until a wooden skewer inserted into the center comes out clean.
While the cake is still warm, poke holes all over the top with a fork.
In a bowl, whisk together the evaporated milk, sweetened condensed milk, and vanilla extract. Pour evenly over the warm cake, allowing it to soak in completely.
Refrigerate for at least 4 hours, or preferably overnight, before serving.
Notes
Enjoy this Tres Leches Cake with a dusting of powdered sugar or a dollop of whipped cream.