In large bowl, beat 1 1/2 cups powdered sugar and the butter with electric mixer on medium speed until smooth. Beat in egg and vanilla until smooth. Beat in flour, baking soda, cream of tartar and cinnamon until well blended. Cover; refrigerate 1 hour or until firm.
Heat oven to 375°F (if using dark or nonstick cookie sheet, heat oven to 350°F). Divide dough in half. On lightly floured surface, roll half of dough at a time 1/4 inch thick. Cut with 2-inch star-shaped cookie cutter. On ungreased cookie sheets, place stars 1 inch apart.
Bake 7 to 8 minutes or until light golden. Cool 1 minute; remove from cookie sheets to cooling racks. Cool completely, about 30 minutes.
In 2-quart saucepan, heat candies and water to boiling over medium-high heat, stirring frequently. Reduce heat to medium-low; simmer uncovered 5 to 6 minutes, stirring frequently, until candies are melted. Remove from heat. With wire whisk, stir in 2 1/2 cups powdered sugar, 1/2 cup at a time, until smooth. Drizzle icing over cookies. (Icing sets up quickly; if necessary, add water, 1 teaspoon at a time, for drizzling consistency.)