Preheat oven to 350°F. Grease an 8 x 8-inch baking pan with nonstick baking spray. Unroll pie crust and line the bottom of the pan with it. Use a sharp knife to gently remove the edges, so the pie only lines the bottom of the pan.
In a stand mixer, combine the eggs, sugar and butter, creaming until light and fluffy. Add vanilla, flour and milk. Mix until combined and pour into crust.
Bake for 40 minutes. Carefully open the oven and sprinkle a layer of cinnamon sugar over the top of the bars. Return to oven and bake for an additional 15-20 minutes, until the center is jiggly but firm.
Allow to cool completely before slicing. Move bars to refrigerator to speed up the cooling process, if necessary.
