In the bowl of a stand mixer fitted with the paddle attachment or with a hand mixer in a large bowl, cream together the butter and sugar. Beat in the vanilla, milk, and flour.
Form the dough into a disk. Place between two sheets of waxed paper on a cutting board. Roll out to 1⁄4 inch thick. I like to peel the waxed paper off the top, then flip the dough over and peel it off the bottom after every few rolls so that it doesn’t stick. Refrigerate for at least 15 minutes.
Using a 2-inch round cookie cutter, cut 24 circles of dough, rerolling as necessary. Place half the dough rounds on top of the other half, for a total of 12. Refrigerate until ready to assemble cups.
Melt the melting chocolate according to the package directions.
Line a standard 12-cup muffin pan with paper liners. Spoon about 1 tablespoon of melting chocolate into the bottom of each liner, enough to coat the bottom. Tap the pan to settle the candy and release any air bubbles.
Place one cookie dough round in each muffin liner. Top with
1 to 2 tablespoons more melting chocolate, spreading as necessary to make sure that the two edges of chocolate meet. Tap the pan again to release air bubbles. Top with sprinkles. Refrigerate until set, about 1 hour. Store in an airtight container in the refrigerator for up to one week. These can also be frozen.