Preheat oven to 325 degrees F. In a large bowl, beat butter with an electric mixer on medium to high speed for 30 seconds. Add powdered sugar and the 1/4 cup crushed peppermint candies. Beat until combined, scraping side of bowl occasionally. Beat in water, vanilla, and peppermint extract until combined. Beat in as much of the flour as you can with the mixer. Using a wooden spoon, 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. Transfer cookies to a wire rack; cool.
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 for 45 to 60 minutes or until glaze starts to thicken.
Spoon about 1 teaspoon of the glaze over each cooled cookie. Sprinkle with additional crushed peppermint candies. Let stand until glaze is set. Makes about 48 cookies.