Line two large baking sheets with nonstick baking mats or parchment paper.

Dip a 2-inch round cookie cutter in flour and mark circles 1 inch apart on the prepared sheets.

Transfer Pate a Choux to a pastry bag fitted with a 5/8-inch plain tip.

Pipe puffs to fit in the floured circles.

Gently smooth the pointed peaks with a moistened finger, rounding tops to ensure even rising.

Freeze puffs (on sheets) until firm, about 30 minutes.

In a saucepan, combine heavy cream, milk, and corn syrup.

Bring to a simmer over medium-high heat.

Remove from heat.

Add finely chopped semisweet chocolate, stirring with a wooden spoon until melted.

Set chocolate sauce aside to cool slightly.

Preheat the oven to 375F.

Remove puffs from freezer.

Bake, rotating sheets halfway through, until puffs are golden brown, 25 to 30 minutes.

Transfer sheets to wire racks to cool completely.

Using a serrated knife, slice off the top third of each puff.

Set aside the tops of the puffs.

Place a scoop of vanilla ice cream on the bottom of each puff.

Replace tops.

Drizzle with chocolate sauce.

Serve immediately.