Preheat the oven to 350°. Lightly grease a 9-by-13-inch baking pan and set aside.
Make the crust: Mix the flour, sugar, nonfat dry milk, baking powder, baking soda and salt together. Then, add the eggs and butter, and mix together to form a sticky ball. Press evenly into the bottom of the pan and set aside.
Make the filling: Set aside 4 tablespoons of confectioners' sugar. Place the cream cheese in a large bowl and whip it to soften using a hand mixer. Gradually add the eggs, the remaining confectioners' sugar and vanilla extract, and blend until smooth. Pour the mixture evenly over the crust in the pan.
Bake on the middle rack of the oven for 40 to 50 minutes, until golden brown. The filling should be "gooey" when removed from the oven. Cool completely and cut into squares. Sprinkle with the reserved confectioners' sugar and serve.