Place racks in the center and upper third of the oven and preheat oven to 425 degrees F. Line two baking sheets with parchment paper and set aside.
In a medium saucepan over low heat, add butter, water, and salt. Cook, stirring occasionally, until the butter is melted. Once butter is melted, add flour and stir to combine. For about 15 seconds you’ll think you’ve made a terrible and lumpy mistake. Keep stirring. After about 30 seconds, the mixture will pull away from the sides and form a ball. Cook for 1 minute more.
Remove dough from the pan and place in the bowl of an electric stand mixer fitted with a paddle attachment. Beat on low speed for 1 to 2 minutes, just to release some of the heat. Add eggs, one at a time, beating for one minute in between each addition. Stop the mixer and scrape down the sides of the bowl after each egg addition. Mixture will be glossy and smooth, thick but still just pourable.
Transfer mixture to a pastry bag fitted with a 1/2-inch found tip.
Pipe mounds onto prepared baking sheets. Mounds should be about 1 1/4-inch wide and 1-inch tall.
Place in the oven and allow to bake for 15 to 20 minutes or until puffed, cooked through and golden brown. Remove from the oven and allow to cool completely on the baking sheets.
While the profiteroles cool, make the chocolate sauce.
Place sugar in an even layer across the bottom of a medium saucepan. Cook sugar (yes… just the sugar) over medium heat until the sugar begins to melt and become golden brown. Don’t stir the sugar, just swirl it to ensure even cooking.
When the sugar has melted to a deep amber color, remove from heat and stir in heavy cream. The mixture will bubble and sizzle, and some of the melted sugar may seize. That’s ok. Return to low heat and stir until any seized sugar has melted. Remove from heat and stir in salt, chocolate chunks, and bourbon. Stir until chocolate is melted. Set aside but keep warm.
To assemble the dessert, slice each profiterole in half. Top one half with a small scoop of ice cream. Place the lid over the ice cream, drizzle with warm chocolate sauce and serve immediately.
The plain profiteroles can we stored in an airtight container for up to 3 days. If they get soft, place them in a warm oven for a few moments to dry them out.