Peppermint Snowballs

Ingredients

• 3 cups all-purpose flour
• 1 teaspoon baking powder
• 1/2 teaspoon salt
• 1 1/2 cups powdered sugar
• 2 1/2 sticks unsalted butter, room temperature
• 1 teaspoon vanilla extract
• 1 egg
• 3/4 cup finely crushed candy canes, divided use
• 1 cup granulated sugar, or as needed
• 2 cups powdered sugar
• 1/4 cup milk