Preheat the oven to 350°F (175°C). Grease a 9×13 inch baking pan and set aside.
In a medium bowl, whisk together the flour, baking powder, and salt. Set aside.
In a large bowl, cream together the butter and sugar until light and fluffy. Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract.
Gradually add the flour mixture to the butter mixture, alternating with the milk, until just combined. Pour the batter into the prepared pan and smooth the top.
Bake for 35-40 minutes, or until a toothpick inserted into the center of the cake comes out clean. Remove from the oven and let cool for 10 minutes in the pan.
While the cake is cooling, make the glaze. In a medium saucepan, melt the butter over medium heat. Stir in the sugar, heavy cream, and vanilla extract. Cook, stirring frequently, until the mixture comes to a boil. Remove from heat and let cool for 5 minutes.
Pour the glaze over the cake, spreading it evenly over the top. Let the cake cool completely in the pan before serving.