Vanilla ice cream:
In a saucepan, bring to a boil the cream, half of the sugar, and the vanilla bean (seeds and pod).
In a bowl, whisk together the egg yolks and the remaining sugar.
While whisking, gradually pour the hot liquid over the egg yolks.
Pour the mixture back into the saucepan and return to medium heat.
Cook for a few seconds until the mixture, now an English cream, coats the back of a spoon.

Remove from heat, add the gelatin, and whisk.
Pour the English cream into a bowl. To avoid condensation, place a sheet of plastic wrap directly on the cream and refrigerate for at least 12 hours.

After 12 hours of refrigeration, remove the vanilla pod and, using an electric mixer, whip until soft peaks form.
Incorporate the chopped chocolate.

Brush a small pastry plate with canola oil and cover the bottom with plastic wrap.
Pour the whipped English cream onto the plate and place in the freezer for at least 12 hours.

Cocoa shortbread:
Using an electric mixer, cream the butter and powdered sugar.
Add the sifted dry ingredients.
Return the mixer to low speed and incorporate, one at a time, the whole egg and the yolk.
Mix until a homogeneous dough forms.
Wrap in plastic wrap and refrigerate for at least 1 hour.

On a lightly floured surface, roll out the dough to about 1/8 inch (3 mm) thick using a rolling pin.

Using a 2-inch (5 cm) round cookie cutter, cut out the shortbread and place them on a baking sheet lined with parchment paper; refrigerate for at least 15 minutes.

Meanwhile, preheat the oven to 350 F (180 C) and bake the cookies for 8 to 10 minutes.
Let cool before assembling the sandwiches.

Assembly:
Unmold the parfait and cut into rounds using the same cookie cutter as for the shortbread.
Assemble the sandwiches by placing a round of parfait on a shortbread and covering with another shortbread.
Store in the freezer in an airtight container for up to 2 weeks.