Combine flour, cocoa, and salt; set aside.
With an electric mixer on medium-high speed, beat butter and sugar until light and fluffy, about 2 minutes. Add egg yolk, milk, and vanilla; mix until incorporated. Reduce mixer speed to low and add the flour mixture until just combined.
Wrap dough in plastic wrap and refrigerate until firm, 1 hour.
With your hands, roll chilled dough into about 25 or 30 1-inch balls. Place balls about 2 inches apart on a baking sheet. With your thumb, gently press down into the center of each ball just slightly to make a small indentation. Place a cherry in each indentation.
Chill the baking sheet of dough balls in the refrigerator for 10 to 15 minutes before baking. {This chilling time makes the cookies bake up soft and tender, and helps minimize spreading. I have skipped this chill before, and the cookies came out on the dry side ... so I don't recommend skipping it.}
Bake at 350℉ until set, about 12 minutes. Let cookies cool on the baking sheet for about 3 minutes, remove to a cooling rack to cool completely.
Place white chocolate and shortening in a small zip-top plastic bag. Set bag in a bowl of warm water to soften. {Don't let the top of the plastic bag get into the water; if water seeps into the bag, the white chocolate will seize up.} Gently knead the chocolate with your fingers until melted and smooth, placing back in the warm water for a minute or two as needed.
Snip a very small hole in the corner of the plastic bag. Drizzle white chocolate over the cooled cookies. Let stand until white chocolate is set.
Store in an airtight container for up to a week.
