Line a 9x13 cake pan with plastic wrap and then parchment paper on top. Scoop the softened vanilla ice cream into the pan. With an offset spatula, smooth it out into an even layer. Freeze the ice cream for at least 4 hours or overnight.
In a large mixing bowl, with an electric mixer on medium, mix together the melted butter and both sugars. Beat until well combined. Add in both eggs and vanilla extract. Mix well.
In another mixing bowl, whisk together the flour, salt, and baking soda. Add the dry ingredients into the wet ingredients and mix well. Fold in both types of chocolate chips. Refrigerate the cookie dough overnight.
When cookies are ready to be baked, preheat oven to 350°. Line a cookie sheet with a silicon mat. Using a 1 oz cookie scoop, scoop the cookie dough into balls about 2 inches apart on the baking sheet. Bake for only 11 minutes or until the edges are slightly golden brown. You want the centers to still be gooey. Place cookies in the freezer to cool off.
When ready for assembly, take out vanilla ice cream from freezer. Using the 3 inch round cookie cutter, cut out rounds of ice cream and sandwich them between two baked and cooled cookies. Press the sandwiches together firmly to get the cookies to stick well to the ice cream round. Roll each sandwich in more mini chocolate chips.
Place sandwiches in the freezer to chill for 2 hours. Allow the sandwiches to thaw slightly before serving.