Preheat oven to 350 degrees F (175 degrees C). Mix leftover cream cheese spread, sour cream, cream cheese, sour cream mixture, and Monterey Jack cheese. Place the layers on the cookie sheet within single layer.
Bake in preheated oven for 35 to 40 minutes. Remove cookie sheet to cool completely, drain on paper towels. Ice cookies while still in plastic bag; cool completely. Cut into squares or dice; place 2 inches apart onto ungreased cookie sheet. Dust with basil.
Cool completely on waxed paper. Fill each edge of each cookie sheet with cream cheese mixture.
Bake for 10 to 12 minutes in the preheated oven, until overbaked. Cool completely on baking sheet.