Choux pastry:
Preheat the oven to 425 F (220 C).
Line two baking sheets with silicone mats or parchment paper.

In a heavy-bottomed saucepan, bring the water, butter, salt, and sugar to a boil.
Once the mixture is boiling, add the flour all at once and stir vigorously with a wooden spoon for 1 minute, until the dough forms a ball that comes away from the bottom of the pan.
Transfer the ball to the bowl of a mixer fitted with a whisk attachment, then add the eggs one at a time, beating rapidly.
The dough should be smooth, but not too soft.
Transfer the dough to a piping bag fitted with a round tip, then deposit small rounds of dough, about 2 inches (5 cm) in diameter, spacing them about 2 inches (5 cm) apart.
Smooth the tops with a damp finger.
Deposit a small amount of coarse sugar on top of the dough rounds.

Bake the choux pastry for 10 minutes, then reduce the oven temperature to 350 F (180 C) and continue baking for 25 minutes.
Remove from the oven and let the choux pastry cool completely on a wire rack.

Strawberry ice cream:
Bring the milk and cream to a boil with the scraped vanilla pod.
Beat the egg yolks and sugar.
Pour the milk and cream mixture over the egg yolks and mix.
Return the mixture to the saucepan and stir with a wooden spoon over low heat, without boiling, until the cream coats the spoon.
Add the strawberry liqueur to the mixture and mix well.

Rinse and hull the strawberries.
Puree the strawberries with the confectioner’s sugar. Strain the mixture if you don’t want any seeds, but it’s not necessary.
Add the strawberry mixture to the cream and refrigerate for at least 2 hours or until the mixture is very cold.
Pour the mixture into an ice cream maker and churn according to the manufacturer’s instructions.

Assembly:
Cut the choux pastry in half. Fill the bottom half of the choux pastry with strawberry ice cream, leaving about twice the height of the pastry.
Place the other half of the choux pastry on top of the ice cream. Repeat with the remaining choux pastry.
Return the profiteroles to the freezer.
Remove them from the freezer 15 minutes before serving, then drizzle with warm chocolate sauce and serve with fresh strawberries.