Heat oven to 375 degrees F. Grease 15 x 10 x 2-inch sheet pan; line with waxed paper; grease paper.
Sift together flour, cocoa powder, baking powder and salt into medium-size bowl.
Beat eggs in medium-size bowl until lemon-colored, about 5 minutes. Gradually beat in sugar until well blended. Beat in milk and vanilla. Fold in flour mixture. Scrape into prepared pan.
Bake in 375 degree F oven for 12 to 15 minutes or until cake springs back when lightly touched.
Meanwhile, spread clean cloth towel on work surface. Sift confectioners sugar-cocoa powder mixture onto towel. When cake is done, invert onto dusted towel. Remove pan and waxed paper. Starting at a short end, roll up towel with cake inside. Place on wire rack and let cool completely.
Soften ice cream in medium-size bowl. Beat in extract and crushed candy canes. Line 13 x 9 x 2-inch pan with plastic wrap. Spread ice cream into plastic-lined pan. Freeze for 15 to 20 minutes.
Once cake has cooled and ice cream is firm, but pliable, unroll cake. Invert ice cream onto cake, leaving 1-1/2-inch border on a short end. Spread ice cream slightly with rubber spatula to edges of cake, leaving the border. Using towel as a guide and starting at the short end of the cake with the border, carefully roll up cake with ice-cream filling inside. Place on wire rack in large pan in freezer.
Place chocolate in medium-size bowl. Bring cream just to simmering in small saucepan. Pour over chocolate in bowl; stir until mixture is smooth, adding peppermint extract if using. Let cool slightly, 3 to 5 minutes or until it registers 85 degrees F on instant-read thermometer. Meanwhile, in plastic bag, finely crush the peppermint candies with a heavy saucepan or rolling pin.
Pour glaze over cake roll, using a spatula if necessary to spread evenly over the roll. Sprinkle the top of the roll with the crushed candies. Place in freezer 4 hours or overnight until frozen. To serve, let stand at room temperature to soften slightly, about 10 minutes. Makes 12 servings.