Weigh and measure all the ingredients. Bring the water to a boil, add the butter, and let it melt in the hot water. Add the flour all at once, stirring constantly. Keep stirring over medium heat until the mixture forms a ball. Dry out the dough over the heat for about 2 minutes, then transfer it to the bowl of a stand mixer.

Add the eggs one at a time, mixing with the whisk attachment. Wait until each egg is fully incorporated before adding the next. Transfer the dough to a piping bag. Pipe out your cream puffs and bake for about 20 minutes at 400°F (200°C). Set aside.

Prepare the vanilla ice cream: Whisk the egg yolks and sugar in a mixer until pale. Heat the milk and vanilla in a saucepan. Add the warm vanilla milk to the egg yolk and sugar mixture. Pour everything back into the saucepan and cook over low heat until it thickens. Let cool, then churn in an ice cream maker. Set aside.

Fill the cream puffs with vanilla ice cream.

Melt the chocolate squares in a double boiler, add the cream, and mix well. Thin the chocolate sauce with the milk until you have a pourable sauce. Arrange the profiteroles on a plate and drizzle with the chocolate sauce.

Toast the sliced almonds in a skillet.