Preheat oven to 350°. Line a baking sheet with a silicone baking mat or parchment paper.
Drain maraschino cherries. Press out any excess liquid using paper towels. Transfer to a food processor and mince into small pieces.
Cream butter and sugar until no longer gritty. Add egg, cherries and extract to butter and mix until well combined.
In a separate bowl whisk together flour, salt, and baking powder. Add to butter mixture and begin stirring with a spoon and then begin using your hands to combine well to form dough. Divide dough in two pucks and cover with plastic wrap. Refrigerate at least an hour, overnight is best.
Pinch off pieces of dough and roll to approximately the size of ping pong balls. Place on prepared cookie sheet and space as they will spread slightly. Keep dough in refrigerator in between baking batches.
Bake 12-15 minutes or until edges begin to turn golden. Remove from oven and rest on cookie sheet 1-2 minutes before transferring to wire cookie racks to cool completely.
Prepare a wire cookie rack with something underneath to catch dripping glaze.
Mix together all glaze ingredients in a small bowl until color is uniform. Either dip cookies into glaze or spoon approximately a teaspoon full onto tops and place onto a wire rack. Allow time to fully set, approximately an hour and a half. Store in an air-tight container.