Crust: Mix cookie crumbs and butter; spoon evenly into 4 half-sheet pans. Place sheet of parchment paper over crumb mixture in one of the pans; use second sheet pan to firmly press crumb mixture onto bottom of pan. Repeat with remaining pans. Bake in 325°F standard oven 10 min.; cool completely.
Cheesecake: Mix strawberry puree and cornstarch in medium saucepan; cook on medium-low heat 6 to 9 min. or until thickened, stirring frequently. Cool.
Beat cream cheese and sweetened condensed milk in 12-qt. bowl of mixer fitted with paddle attachment. Beat 1 to 2 min. or until well blended; scrape down side of bowl. Blend in lemon juice and vanilla. Add eggs, 1 at a time, beating after each just until blended. Pour evenly over crusts. Drop strawberry mixture by spoonfuls over batter. Gently swirl with knife or spatula.
Bake 30 to 32 min. or until centers of cheesecakes are almost set, rotating pans after 15 min. Cool completely. Cut into 4x8 yielding 32 pieces each half sheet pan.