Pour Armagnac over prunes; cover and soak for at least 1 day or up to 1 week at room temperature. Drain, reserving liquid.

Let ice cream stand at room temperature until soft enough to fold in ingredients, about 15 minutes; fold in prunes. Cover and return to freezer. Freeze until hard, about 3 hours or for up to 1 week.

Chocolate Sauce: In saucepan over medium-low heat, melt bittersweet and milk chocolates and butter in milk, stirring; when smooth, stir in sugar and cream. Bring to boil, stirring. Remove from heat; stir in 2 tbsp (30 mL) of the reserved Armagnac mixture. (Make-ahead: Refrigerate in airtight container for up to 1 month; microwave or warm over low heat until pourable.)

In saucepan, bring 1 cup (250 mL) water, butter, sugar and salt to boil over medium heat. Remove from heat and add flour all at once; stir with wooden spoon to form ball of dough and return to heat. Cook, stirring continuously, until thickened and slightly dry, with film appearing on bottom of pan, about 3 minutes.

Transfer to bowl; let cool for 3 minutes. Using electric beater on low speed or with wooden spoon, beat in 1 egg until fully incorporated. Repeat with remaining eggs, beating until dough is smooth and shiny.

Place generous tablespoonfuls (15 mL) of dough on parchment paper–lined baking sheet 2 inches (5 cm) apart. Bake in 400F (200C) oven until puffed and golden brown, 16 to 18 minutes. (Make-ahead: Let cool; store in airtight container at room temperature for up to two days.) Makes 24 pieces.

For each serving, split open 2 profiteroles and fill with small scoop of ice cream. Replace tops and drizzle with chocolate sauce.

Makes 12 servings.