In a large mixing bowl, beat the butter with an electric mixer on medium to high speed for 30 seconds. Add powdered sugar and the ¼ cup crushed candies. Beat until combined, scraping sides of the bowl. Beat in the water, vanilla and peppermint extract until combined. Beat in as much of the flour as you can with the mixer. Stir in any remaining flour.
Shape dough into 1-inch balls. Place 1 inch apart on an ungreased cookie sheet. Bake about 15 minutes or until bottoms are lightly browned. Let cool a bit, then transfer to a rack to cool completely.
Meanwhile, for glaze, in a medium saucepan bring whipping cream just to simmering. Remove from heat. Add white chocolate; let stand for 3 minutes. Stir until smooth. Let stand about 45 minutes or until glaze begins to thicken (put in the refrigerator for a bit if it seems too thin).
Spoon about 1 teaspoon of the glaze over each cooled cookie. Sprinkle with more crushed candy. Let stand until glaze is set.