For the Cookies: Preheat oven to 350 degrees F.
Cream together the butter and sugars.
Add in the eggs, one at a time. Add in vanilla. Mix well.
Sift together the flour, baking soda, and salt. Add to the butter, and mix just till combined.
Fold in 1/2 cup of sprinkles and 1 1/2 cups mini chocolate chips.
Roll the dough into tablespoon sized balls. Place 2 inches apart on a parchment lined baking sheet. Bake for 8 to 12 minutes till lightly browned.
Cool on cookie sheet for about 5 minutes. Transfer to a wire rack and cool completely.
For the Ice Cream: Whisk together all ingredients in a sauce pan. Cook over medium heat till mixture reaches 160 degrees F, whisking constantly. Let cool and chill in the freezer till very cold.
Pour mixture into ice cream maker and prepare according to manufacturer’s directions.
Line a 13 x 9 inch baking pan with plastic wrap or waxed paper. Pour ice cream mixture into the dish and spread out evenly using a spatula. Freeze until hardened (at least 4 hours, preferably overnight).
In a small shallow dish, combine 1 cup of mini chocolate chips with 1/2 cup rainbow sprinkles.
Using a round cookie cutter about the same size as your cookies, cut out circles of ice cream and sandwich them between 2 cookies. Roll the outside edge of each ice cream sandwich in the sprinkles and mini chocolate chips. Wrap in wax paper and freeze.