Put the first 8 ingredients in a large bowl and stir until well blended. Add butter and work with your fingers until a crumbly texture is achieved.
Make a well in the center and add the remaining ingredients. Stir with a large wooden spoon to combine. The dough will be sticky. Add extra milk, if necessary, to ensure that the dough holds together.
Cover and refrigerate for 1 hour or overnight.
Preheat oven to 375 degrees. Scoop dough by the tablespoonful and shape it into balls. Place on a parchment-lined baking sheet. Bake for 12 to 13 minutes.
Don't overbake - these are meant to be soft and moist. Remove from sheets and cool completely on racks.
Combine the Icing ingredients in a bowl until just smooth. You want it more thick than thin, but still runny.
Dip the tops of the cooled cookies into the glaze, then return to the wire rack, allowing the glaze to drip down the sides of the cookie.
Top with sprinkles while glaze is still wet. Store in an airtight container.