Heat the broiler and line a baking sheet with greased foil. Spread 2 cups mini marshmallows in a single layer and broil for 1 to 2 minutes, watching closely, until deeply golden and toasted. They go from golden to burnt quickly, so do not walk away.
Warm the milk in a small saucepan over low heat until steaming. Scrape the toasted marshmallows into the milk with a greased spatula and stir until fully melted and smooth, then let cool for 20 minutes.
Place a 9x5-inch loaf pan in the freezer. Add the marshmallow mixture, cottage cheese, sweetened condensed milk, vanilla and salt to a high-speed blender and blend for 1 to 2 minutes until completely silky.
The toasted marshmallows give real campfire flavor and help the ice cream stay smooth and scoopable. In a large chilled bowl, whip the heavy cream with a hand mixer until stiff peaks form, about 2 to 3 minutes.
Stir a large spoonful of the marshmallow mixture into the whipped cream to lighten it. Gently fold in the rest until smooth.
Fold in the graham cracker pieces, chopped chocolate and remaining 1/2 cup mini marshmallows. Spread into the chilled pan, press plastic wrap onto the surface and freeze for at least 6 hours or overnight.
Let the ice cream soften at room temperature for 10 minutes before scooping.