Preheat the broiler. Pour 1/2 cup heavy cream into a medium saucepan and set aside. Line a baking sheet with nonstick foil. Spread all but 1 cup marshmallows on the prepared pan. Broil until toasted, 30 seconds to 1 minute. Scrape the marshmallows into the saucepan of heavy cream using a spatula. Cook over medium heat, stirring constantly, until smooth and darkened in color, 6 to 9 minutes. Let cool, about 1 hour.
Meanwhile, preheat the oven to 350˚. Line a 9-by-13-inch straight-sided baking pan with a double layer of foil, leaving a 2-inch overhang on the two long sides; coat with cooking spray. Mix the graham cracker crumbs, melted butter, 1/3 cup sugar and the salt in a large bowl with a fork. Press evenly and firmly into the pan. Bake until toasted, 10 to 12 minutes. Let cool completely, about 30 minutes.
Beat the cream cheese, remaining 1/2 cup sugar and vanilla in a large bowl with a mixer on low speed, 1 minute. Increase the speed to medium high and beat until light and fluffy, 2 minutes. Reduce the speed to low and beat in 1 cup heavy cream, then increase the speed to medium high and beat until stiff peaks form, about 2 minutes. Reduce the speed to low again and beat in the cooled marshmallow cream, then increase the speed to medium and beat until light and fluffy, 1 to 2 minutes. Spread evenly over the crust and refrigerate until mostly set, about 2 hours.
Put the chocolate in a small bowl. Heat the remaining 1/2 cup heavy cream in a saucepan over medium heat until just simmering. Pour over the chocolate and let stand 5 minutes, then stir until smooth. Spread the warm chocolate mixture over the cheesecake layer. Refrigerate until fully set, at least 6 hours or overnight.
Preheat the broiler. Run a thin knife along the two short sides of the pan to loosen, then lift out the cheesecake using the foil overhang. Remove the foil and cut into squares.
Line a baking sheet with nonstick foil. Place the reserved 1 cup marshmallows on the foil; broil until toasted, 30 seconds. Top each cheesecake bar with a few toasted marshmallows.