Nutella and Raspberry Swirl Ice Cream Cake with Ice Cream Cone Crust



About 15 regular-sized ice cream cones
⅓ cup butter, melted
2 cups whipping cream
1 14oz can sweetened condensed milk
1 cup thick chocolate syrup
½ cup plus ¼ cup Nutella, divided
3 tbsp plus ⅛ cup milk or cream, divided
½ cup raspberry preserves
Whipped cream and fresh raspberries for garnish if desired