Preheat oven to 325 degrees. Prepare a 10 inch tall-sided tart pan or 9 inch springform pan (see note below about pans), by lightly greasing the bottom and sides.
To make the filling, beat the cream cheese on medium speed in a stand mixer fitted with the paddle attachment, for several minutes until light and fluffy. Scrape down the sides of the bowl. Add the powdered sugar and mix for several minutes until light and fluffy. Scrape down the sides of the bowl again. Add the egg and scrape down the sides as needed. Mix in the butter, lemon extract, vanilla and zest. Do not overmix. Set aside.
To make the cake, in a large bowl, whisk together the flour, sugar, baking powder and salt. In another bowl, whisk the cooled butter, eggs, lemon juice, vanilla extract, and zest. Whisk the the butter mixture into the flour mixture, just until combined. Do not over mix.
Spread cake batter evenly into prepared pan. Pour cream cheese filling mixture over the top of the cake batter until it reaches 1/2 inch from the side. You should see a cake batter border 1/2 inch around the filling.
Bake for 30-35 minutes or until a toothpick inserted near the edge of the pan comes out clean. (Be sure to watch carefully at the end because it is very easy to overcook.) Cool on a wire rack for 10 minutes, remove edge of pan. Cool for an additional hour, and then refrigerate until cold. Serve with a light dusting of powdered sugar.