Pre-heat the oven to 350°F; lightly grease a 13 x 9-inch baking pan.
Unroll one can of crescent rolls and press it into the bottom of the prepared pan, pinching the seams together to form a smooth, even layer.
In a medium bowl, beat cream cheese, sugar, vanilla extract and egg until smooth and creamy.
Spread this mixture evenly over the crescent roll layer.
Unroll the second can of crescent rolls and place it over the cream cheese mixture: pinch the seams together to seal.
Brush the top layer with the egg white.
Place in the pre-heated oven and bake for 35 to 45 minutes or until the top is golden brown.
Remove from the oven and allow to cool for 20 minutes.
While the Danish is cooling, using a small bowl, whisk together confectioners' sugar, milk and vanilla extract until smooth
Drizzle the glaze over the cooled Danish.