In a heavy saucepan, melt chocolate and butter over low heat. Stir in milk and sugar. Cook and stir for 8 minutes or until sugar is dissolved. Remove from the heat; stir in vanilla. Cool completely.
Spread half of the ice cream into pastry shell; freeze until firm. Spread half of the chocolate mixture over ice cream; freeze until set. Repeat layers. Freeze for several hours or overnight.
In a heavy saucepan, combine the egg whites, sugar, water and cream of tartar. With a hand mixer, beat on low speed for 1 minute. Continue beating over low heat until mixture reaches 160°, about 12 minutes.
Pour into the bowl of a heavy-duty stand mixer; add vanilla. Beat on high until frosting forms stiff peaks, about 7 minutes. Fold in peppermint candy. Spread over top of pie. Cover and freeze until serving. Pie may be frozen for up to 2 months. Yield: 6-8 servings.