Preheat the oven to 350 degrees.
Microwave the butter for about 40 seconds to just barely melt it. If there is still a piece of butter that isn't melted then swirl it until it melts {you don't want the butter to be hot or the eggs will curdle}.
Add both sugars and mix until creamy {by hand works great}. Add the vanilla and the egg, mix until incorporated but do not over mix or the dough will be stiff.
Add the flour, baking soda, and salt. Mix until everything is incorporated. Add the chocolate chips and stir until they are evenly distributed.
Scoop the dough with a medium scoop {or about 2 tablespoons} into your hand and roll until smooth. Place on a silicone {or parchment} lined baking sheet and add a few additional mini chocolate chips to the top {if desired}.
Bake for 9-11 minutes. You want to remove them from the oven when they are puffy and just starting to turn golden. The key to getting the super soft cookie is to not over bake them. Once you remove them from the oven add a few additional mini M&M's to the top of each cookie and let them cool completely on the cookie sheet {if you can wait that long}. This will allow them to set up perfectly.
While the cookies are baking scoop the ice cream onto a quarter sheet pan {or 9x13 pan} and spread into an even layer. Freeze for at least 30 minutes. After it is refrozen, remove the ice cream from the freezer and cut 12, 3 inch circles.
Turn half of the cookies on their tops and add a circle of ice cream. Then top with the remaining cookies. Freeze until ready to eat. Store in freezer for up to 2 months.