Spread Nutella over one side of each slice of bread. Assemble the slices into sandwiches, Nutella sides together.
In a large bowl, whisk together the eggs, milk, and vanilla extract. Pour the crushed graham crackers on a rimmed plate.
In a skillet, melt 1 tablespoon of the butter over medium low heat.
Dip a sandwich into the egg mixture and coat thoroughly. Allow the excess to drip off, then coat thoroughly in the graham cracker crumbs. Place in the heated skillet and cook until golden, about 1 minute. Flip and cook the other side, then the edges briefly. Transfer to a baking sheet, then repeat with remaining sandwiches, adding more butter as needed.
Top the prepared French Toast with marshmallow halves or mini marshmallows and place the baking sheet under a broiler set on low until the marshmallows are melty and toasted (this happens quickly, keep an eye on it).
Serve immediately drizzled with the chocolate sauce and mini chocolate chips.