Preheat the oven to 350°F (175°C). Grease and flour a 9×13-inch baking pan.
In a medium bowl, whisk together the all-purpose flour, baking powder, and salt. Set aside.
In a large bowl, beat the softened butter and granulated sugar together with an electric mixer on medium speed until light and fluffy, about 3-5 minutes.
Add the eggs one at a time, beating well after each addition.
Mix in the vanilla extract.
Alternately add the flour mixture and whole milk to the butter mixture, beginning and ending with the flour mixture. Mix each addition just until combined; do not overmix.
Pour the batter into the prepared baking pan and smooth the top with a spatula.
Bake for 38-42 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and allow it to cool in the pan on a wire rack for 15 minutes.
While the cake is cooling, prepare the vanilla glaze by whisking together the melted butter, powdered sugar, whole milk, and vanilla extract in a small bowl until smooth.
Poke holes all over the top of the warm cake using a skewer or fork, then pour the glaze evenly over the cake, allowing it to soak in.
Let the cake cool completely before slicing and serving.