Mix graham cracker crumbs, butter, and 1/3 cup sugar in a bowl. Press mixture into the bottom and up the sides of a 9- to 10-inch springform pan to form crust.
Preheat oven to 350 degrees F (175 degrees C).
Place caramels and milk in a small saucepan over medium heat; stir until smooth, 5 to 8 minutes. Stir in pecans; pour mixture into the crust. Refrigerate until ready to use.
Melt chocolate in a microwave-safe bowl in 15-second intervals, stirring after each melting, 1 to 3 minutes. Let cool slightly.
Beat cream cheese in a bowl using an electric mixer on high speed until light and fluffy. Add 3/4 cup sugar, eggs, and vanilla extract. Stir in the melted chocolate. Beat until well blended; pour cheesecake filling into the crust.
Bake in the preheated oven until center is almost set, 40 to 50 minutes. Cover cheesecake and refrigerate for at least 3 hours.