Preheat oven to 350°F. Spray a 9×13-inch glass baking dish with nonstick cooking spray.
Unroll a full sheet of crescent dough and press into the bottom and up the sides of the prepared baking dish, pressing the seam lines together.
In a medium mixing bowl, beat together softened cream cheese, 1 teaspoon vanilla extract, lemon juice, granulated sugar, and 1 egg. Spread mixture evenly over the crescent dough.
Roll out the second sheet of crescent dough, pressing seams together with your fingers. Lay dough over the top of the cream cheese layer.
Mix remaining egg with a tablespoon of water and brush over the top of the crescent dough top.
Bake for 30 to 40 minutes or until crescent dough is golden brown on the top and on the bottom of the baking dish.
Allow the cheese danish to cool for 20 to 30 minutes before topping with glaze.
To make the glaze, whisk together ½ cup powdered sugar, remaining ½ teaspoon vanilla extract, and milk until smooth.
Drizzle glaze over cooled danish.
Cut into 12 bars and serve.