1. Heat oven to 325ºF. Place cookies in bowl of food processor. Pulse 30 seconds, or until finely ground. (Or, place cookies in zip-top bag and using the bottom of a heavy skillet, pound cookies until finely crushed); transfer cookie crumbs to bowl (there should be about 2 cups). Add butter, stirring until combined. Transfer cookie mixture to 9" spring form pan. Using your fingers, press cookie crumbs evenly onto bottom and sides of pan. Bake until firm and fragrant, 7 - 10 minutes; cool.
2. In bowl of electric mixer on medium speed, beat cream cheese until fluffy, about 3 minutes. Add condensed milk; beat until smooth, 1 minute. Beat in eggs, vanilla and 3 tablespoons dulce de leche until combined, 3 minutes. Pour filling into prepared crust. Bake until golden brown and set, but still wiggly in the middle, 45 - 55 minutes. Turn off oven; partially open oven door. Let cake sit in oven until room temperature, about 1 hour. Transfer cake to refrigerator; cool completely, at least 4 hours.
3. Remove cheesecake from pan. Place remaining dulce de leche in zip-top bag. Using scissors, snip small hole in corner of bag. Applying even pressure on "pastry bag," make swirly designs on top of cake; slice and serve.