Preheat oven to 350 degrees. Coat a 9-inch by 13-inch cake pan with nonstick spray.
In a large bowl, combine cookie mix, pudding mix, brown sugar, butter, 1 teaspoon vanilla, and 1 whole egg. Mix well and press in to bottom of pan.
In a standing mixer with the paddle attachment, or in a large bowl by hand, beat cream cheese, sour cream, and sugar until smooth.
Add remaining whole egg, egg yolks, and remaining 1 1/2 teaspoons vanilla. Beat until smooth. Pour over crust in pan and smooth the top.
Bake for 35 to 45 minutes or until center is set. Cool at least 30 minutes. Store in the refrigerator.