Preheat oven to 350ºF. Grease a 9x13-inch baking pan.
For cake, combine flour, baking powder, and salt in a medium bow. In a large bowl, whisk together sugar, melted butter, and egg. Add flour mixture and mix with a wooden spoon until dough is moist and crumbly. Spread dough evenly in a prepared pan.
For topping, a in a medium bowl, beat cream cheese with an electric mixer until smooth. Beat in eggs and vanilla. Reserve 2 tbsp on confectioner's sugar. With beaters on low speed, mix remaining confectioner's sugar into cream cheese mixture. Mix in melted butter until fully blended.
Pour topping over dough and spread it evenly with a rubber spatula. Bake for 40-45 min or until topis set with a nicely golden crust, but inside is still slightly gooey and soft. Remove from oven and cool completely. Cut into squares. Just before serving, sprinkle with reserved 2 tbsp confectioner's sugar.