Preheat the oven to 400 degrees F and line 2 baking sheets with parchment paper.
To make the pate a choux: In a heavy-bottomed saucepan, bring the water, butter, sugar, and salt to a gentle boil over medium-high heat, stirring to melt the butter completely. Add all the flour and baking powder at once and continue to stir until all the flour is incorporated and the dough becomes a mass that pulls away from the sides of the pot. Remove from the heat and scrape the dough into a mixing bowl. Using a standing or hand-held mixer, beat the dough on medium speed to cool it off a bit. Add the eggs, 1 at a time, stopping to scrape down the sides of the bowl periodically. When all eggs have been incorporated, the dough should be a thick, smooth, and glossy paste.
Form 24 golf ball-size mounds on the lined baking sheet about 2-inches apart allowing room for them to spread; keep the mounds as high and round as possible. You can use a pastry bag fitted with a star tip or a large spoon, your choice. Place the pans in the oven and bake for 10 minutes. Reduce the heat to 350 degrees F. and continue to cook for 25 minutes. Do not open the oven door or remove the pans from the oven until the puffs are firm to the touch. The profiteroles should be golden brown and well-risen. Allow the shells to cool before filling.
Using a serrated knife, slice the pastry puffs almost in half. Place 3 profiteroles on each dessert plate and fill with a scoop of ice cream. Drizzle the chocolate sauce over the top; garnish with confectioners' sugar and fresh mint, if desired.
Combine the cream and butter in a small heavy-bottomed saucepan over medium heat. Heat the mixture until bubbles appear around the sides of the pot, but do not allow the cream to boil. Mix in the chocolate and vanilla; remove from the heat and stir until the chocolate melts and the sauce is smooth. May be served warm or chilled.