Heat oven to 350°F. Spray 13x9-inch (3-quart) glass baking dish with cooking spray.
Press sugar cookie dough in bottom of baking dish. Bake 10 to 15 minutes or until lightly set. Cool completely, about 15 minutes.
In large bowl, beat cream cheese and sugar with electric mixer on medium speed until smooth. Beat in vanilla, then eggs, one at a time, scraping side of bowl between additions. Beat in mashed bananas.
Pour over cooled crust. Bake about 30 minutes or until outer edges of cheesecake are set. Cool completely, about 15 minutes, then refrigerate 30 minutes before cutting. For bars, cut into 5 rows by 3 rows. Cover and refrigerate any remaining bars.