For Ice Cream: Place ice cream in large bowl. Fold in candies and peppermint extract. Cover and freeze until ice cream is firm, at least 4 hours. (Ice cream can be made 1 week ahead. Keep ice cream frozen.).
For Cream Puff Pastry: Preheat oven to 400 degrees. Line heavy large baking sheet with parchment. Combine 3/4 cup water, butter, sugar and salt in heavy medium saucepan. Bring to boil, stirring until butter melts. Add flour and stir over medium heat until dough pulls away from sides of pan and forms ball, about 2 minutes. Cool 10 minutes.
Using electric mixer, beat 3 eggs into dough 1 at a time. Transfer dough to pastry bag fitted with 1/2-inch plain tip. Pipe sixteen 1-1/2" mounds of dough onto sheet, spacing about 2 inches apart. Beat 1 egg in small bowl. Brush over dough mounds (do not drip egg onto sheet).
Bake pastries 20 minutes. Reduce oven temperature to 350 degrees. Bake pastries until golden brown, about 10 minutes. Using skewer, pierce side of each pastry to allow steam to escape. Bake pastries 5 minutes longer; transfer to racks and cool completely. (Pastries can be made 1 week ahead. Enclosde pastries in resealable plastic bag; freeze. Thaw pastries before continuing.).
For Chocolate Sauce:.
Bring cream to a simmer in a heavy medium saucepan. Remove from heat. Add chocolate. Let stand until chocolate softenes, about 5 minutes. Whisk until smooth. (Can be made 2 days ahead. Cover and chill. Rewarm over low heat.).
To assemble: Cut pastries crosswise in half. Place 1 scoop of ice cream onto bottom of each pastry. Cover with pastry tops. Spoon some warm chocolate sauce into 8 bowls. Place 2 profiteroles atop sauce in each bowl. Spoon sauce over profiteroles. Sprinkle with additional crushed peppermints and garnish with mint sprigs.