Preheat oven to 400°F (200°C). Line two baking sheets with parchment paper.

In a large saucepan, combine water, butter, salt, and 1 tbsp granulated sugar. Bring to a rolling boil over medium-high heat, stirring until the butter is completely melted.

Remove the saucepan from heat. Add the sifted all-purpose flour all at once. Stir vigorously with a wooden spoon until a ball of dough forms and pulls away cleanly from the sides of the pan.

Return the pan to medium heat and continue to stir the dough for 1-2 minutes to dry it out. A thin film should form on the bottom of the pan.

Transfer the hot dough to a stand mixer bowl (or a large mixing bowl if mixing by hand). Let it cool for 5 minutes, stirring occasionally, until it's warm but not hot (you should be able to comfortably touch it).

With the mixer on low speed (using a paddle attachment) or by hand, gradually add the lightly beaten eggs, a little at a time, ensuring each addition is fully incorporated before adding the next. The dough will look curdled at first but will come together to form a smooth, shiny, thick paste. It should be firm enough to hold its shape but soft enough to pipe (when a spoon is pulled through, it should leave a soft V shape).

Transfer the choux pastry to a piping bag fitted with a 1/2-inch (1.25 cm) round tip. Pipe 1-inch (2.5 cm) mounds onto the prepared baking sheets, leaving about 2 inches (5 cm) between them. Alternatively, use two spoons to drop rounded tablespoons of dough.

Dip your finger in a little water and gently smooth down any peaks on the piped choux to prevent burning.

Bake for 15 minutes at 400°F (200°C).

Reduce oven temperature to 350°F (175°C) and bake for another 20-25 minutes, or until the profiteroles are golden brown, puffed, and feel light and hollow. Crucially, do not open the oven door during the first 25 minutes of baking.

Turn off the oven, prop the door open slightly with a wooden spoon, and let the profiteroles dry out in the cooling oven for another 10-15 minutes. This step is essential to help prevent them from collapsing.

Remove from oven and transfer to a wire rack to cool completely. Once cool, they can be stored in an airtight container at room temperature for up to 1 day, or frozen for longer.

In a small saucepan, combine heavy cream, 1/4 cup granulated sugar, cocoa powder, and a pinch of salt. Whisk well to combine.

Bring the mixture to a gentle simmer over medium heat, stirring constantly, until the sugar is dissolved and the sauce is smooth.

Remove from heat. Add the finely chopped bittersweet chocolate and 1 tbsp unsalted butter. Whisk until the chocolate and butter are completely melted and the sauce is smooth and glossy.

Stir in the vanilla extract. Keep the sauce warm or reheat gently before serving.

Just before serving, slice each cooled profiterole in half horizontally.

Fill each profiterole bottom with a small scoop of slightly softened vanilla bean ice cream. Replace the top half.

Arrange the filled profiteroles on individual serving plates or a large platter.

Generously drizzle with the warm chocolate sauce. Serve immediately for the best experience.