Line 9-inch square baking pan with foil. Spray foil with no stick cooking spray. Place chopped chocolate in large bowl. Set aside.
Bring sweetened condensed milk and cream to simmer in medium saucepan on medium heat, stirring frequently with wire whisk. Pour over chopped chocolate. Let stand 1 minute. Whisk until chocolate is melted and mixture is smooth. Stir in peppermint extract. Remove 3/4 cup chocolate mixture. Tint chocolate mixture pink with red food color.
Pour remaining (plain) chocolate mixture into prepared pan. Drop tinted chocolate mixture by tablespoons over chocolate mixture in pan. Swirl with knife for marble effect.
Refrigerate 4 hours or overnight until firm. Cut into 36 squares. (May be made ahead. Store chocolate mixture, tightly covered, in pan in refrigerator up to 2 weeks. Bring to room temperature before cutting into squares.).
To assemble chocolate on a stick, thread a marshmallow half and a chocolate square onto each lollipop stick. Wrap each hot chocolate on a stick in plastic wrap or small cellophane bag. (May be assembled up to 2 days ahead.).
To serve, stir hot chocolate on a stick into 8 ounces hot milk.