1. Preheat oven to 200°. Line a baking sheet with parchment paper. Using an electric mixer, beat egg whites and salt on medium-high speed until white and foamy, about 1 minute. With mixer running, gradually add suger in 3 additions beating for 2 minutes between each addition. Beat until firm peaks form, about 2 minutes longer. Add powdered sugar and peppermint extract; beat to blend, about 1 minute.
2. Dot coloring over surface of meringue; do not stir (the coloring will form swirls when piped). Spoon meringue into a pastry bag fitted with a 1/2" tip. (See Prep School; alternatively, spoon into a plastic freezer bag, then cut 1/2" off 1 corner.) Twist top; pipe 1" rounds onto prepared sheet, spacing 1" apart.
3. Bake meringues until dry, about 2 1/2 hours. Let cool completely, about 1 hour (meringues will crisp as they cool).
4. Can be made 2 days ahead. Store airtight at room temperature between sheets of parchment or waxed paper.