Chop and crush 14 graham crackers in a small bowl; crush remaining 4 crackers in a separate bowl and set aside. Mix 1/4 cup sugar and melted butter into the crushed 14 graham crackers. Press crust into the bottom of a 9x13-inch baking dish.

Beat remaining 1 cup sugar, cream cheese, and vanilla extract together using an electric mixer in a bowl until well blended. Beat in eggs until well blended. Mix in 1/2 the chocolate. Pour batter into the pan over the crust. Sprinkle remaining 1/2 of the chocolate, marshmallows, and reserved graham crackers on top. Drizzle with caramel.

Bake in the preheated oven until golden and set, 40 to 45 minutes. Remove from the oven and let cool completely, 15 to 30 minutes.

Refrigerate at least 3 hours, to overnight. When ready to serve, cut into square bars.