In a large bowl, cream butter until it is light and fluffy, about 1 minute. Add in brown sugar and white sugar and beat until well combined, scraping down the sides of the bowl as necessary.

Next, add in the egg, beating well. Add in vanilla extract and salt; mix.

Sift together flour, baking soda, corn starch, and espresso powder. Gradually add the dry ingredients into the wet ingredients, stirring until just combined.

Add in chocolate chips. Stir.

Chill dough for about 30 minutes.

Preheat oven to 350 degrees and line two baking sheets with parchment paper or grease with cooking spray.

Take about 2 Tbsp of dough and flatten it slightly in your hand. Stick 2-3 marshmallows in the center, and fold the cookie dough around the marshmallows and form it into a ball. Make sure none of the marshmallows can be seen in the dough. Repeat until all dough is gone (dough should make 12 large cookies).

Place dough onto cookie sheets, about 2-3 inches apart.

Bake for 15-16 minutes, or until cookies are barely turning golden brown (in order for the cookies to remain soft after being in the freezer, they need to be slightly underdone).

If desired, add a couple more marshmallows on top of each cookie as they cool.

Allow to cool completely.

While the cookies are chilling, form the ice cream into discs. Take a 1 cup measuring cup, or something of similar size (like pictured above), and place plastic wrap inside of it, making sure some is hanging over the sides. Scoop 1/2 cup of ice cream into the plastic wrap, and press it into the cup, making a flat, even layer. Take the ice cream out, wrapping the plastic wrap securely around it, and place in the freezer. Repeat for the meaning ice cream (in total, you should have six ice cream centers).

Once the cookies have cooled, dip each cookie into the melted milk chocolate (which can be done in the microwave in 30-second intervals or over a double broiler) about halfway. Lay each cookie down on parchment paper and sprinkle with graham cracker crumbs. Allow chocolate to cool, about 30-60 minutes at room temperature, or 15-20 minutes in the refrigerator.

Once the chocolate has cooled, place six cookies face down onto a cookie sheet. Unwrap each ice cream center and place one on each cookie. Take the remaining six cookies and place them on top.

Enjoy immediately or wrap in plastic and store in the freezer until ready to eat them!