In a stand mixer fitted with the paddle attachment, cream the butter and sugar together until smooth, about 1 minute. Add the vanilla, almond extract, flour, salt, and milk, mixing until combined. Stir in the sprinkles. Chill for 20 minutes.

Roll the cookie dough into small balls, then place on a parchment-lined baking sheet. Chill in the freezer while you work on the ice cream and frosting.

In the bowl of a stand mixer, fitted with the whisk attachment, beat egg yolks, sugar, and salt on high speed until yolks lighten in color and thicken into a ribbon as you lift the whisk out of the bowl, about 2 minutes.

In a medium saucepan combine milk and heavy cream. Stir over medium heat and bring to a simmer, about 5 minutes. With mixer on low, gradually pour 1 cup of warm liquid into egg mixture. Add egg mixture to saucepan. Stir and and continue to cook over medium heat until mixture begins to bubble slightly and is thick enough to coat the back of a wooden spoon.

Immediately pour custard mixture through a fine mesh sieve over a bowl or large glass measuring cup. Whisk in the extracts. Cover and chill the mixture thoroughly in the refrigerator* while you make the frosting.

In a stand mixer fitted with the paddle attachment, cream the butter, cream cheese, and salt together until smooth and creamy. Add the vanilla, almond extract, powdered sugar, and milk, beating until combined.

Divide the frosting into 3 small bowls. Dye each frosting with desired color.

Once the custard mixture is chilled, freeze in an ice cream maker, following the manufacturer's instructions.

Once ice cream is done churning, stir in most of the cookie dough balls by hand, reserving 15-20 balls for the very end. Pour a third of the mixture into a freezer-safe container. Spoon blobs of a third of the frostings evenly over the ice cream. Add another third of the ice cream on top, followed by a third of the frosting. Pour the remaining ice cream on top, and spoon the rest of the frosting evenly over ice cream. Swirl the frosting into the ice cream with a skewer or butter knife.

Top with remaining cookie dough balls and sprinkles. Freeze for at least 6 hours, preferably overnight. Scoop and enjoy!