How to Make It
Whisk together cornstarch, salt, and 3/4 cup of the sugar in a medium-size heavy saucepan. Whisk together half-and-half, heavy cream, egg yolks, and vanilla bean paste in a small bowl; gradually add to cornstarch mixture, whisking constantly.
Bring mixture just to a boil over medium, whisking constantly, about 15 minutes. Boil, whisking constantly, 1 minute. Remove from heat, and transfer to a bowl. Cover with plastic wrap, placing plastic wrap directly on mixture in bowl; chill 4 to 24 hours.
Preheat oven to 350°F. Pulse crushed cookies and chocolate in a food processor until finely ground, 8 to 10 times. Transfer to a bowl, and stir in butter and remaining 1/4 cup sugar. Firmly press mixture on bottom, up sides, and onto lip of a lightly greased (with cooking spray) 9-inch round pie pan. Bake in preheated oven 10 minutes. Transfer to a wire rack, and cool completely, about 30 minutes.
Spoon chilled half-and-half mixture into prepared crust. Freeze 2 hours. (Pie may be frozen up to 24 hours.)
Toss together strawberry halves, blueberries, blackberries, and raspberries in a medium bowl. Arrange berries on top of pie. Top with 3 whole strawberries. (If pie was frozen longer than 2 hours, top with berries, and let stand 1 hour before brushing with jelly mixture.)
Melt jelly in a small microwave-safe bowl at HIGH, stirring every 15 seconds, until melted, about 1 minute. Stir in water. Brush jelly mixture gently over berries.