To make the cake: Preheat oven to 350°F and butter a cake pan.
Sift together flour, baking powder, baking soda, and salt.
Heat butter and sugar in a large bowl with an electric mixer at medium speed until pale, then add vanilla.
Add eggs, 1 at a time, beating well after each addition. At low speed, beat in milk and dulce de leche until combined.
Add flour mixture in 3 batches, mixing until each addition is just incorporated.
Spread batter in cake pan. Bake in center of oven until a wooden toothpick inserted in center of cake comes out clean, about 40 minutes.
Cool in pan on a rack for 10 minutes, then run a knife around edge of pan. Invert onto rack and cool completely, about 45 minutes.
To make the glaze: Place cream, dulce de leche, vanilla and a pinch of salt in a small saucepan over medium heat, stirring often and cook for 10 minutes.
Pour hot glaze over top of cake, allowing it to run down sides.