Cream sugar and butter in a large bowl; beat in egg, milk, and vanilla. Stir in dry ingredients.
Roll about 2 teaspoons of dough around each cherry.
Place on greased cookie sheets and bake at 350° for about 10 minutes. Cool completely.
Melt the chocolate chips in a small ziplock bag in the microwave at half power. Check often and squish the chocolate so that it melts evenly and doesn't burn.
Snip off a tiny corner of the bag and drizzle chocolate over the cooled cookies.