Preheat the oven to 425 degrees F.
Heat the milk, butter, and salt over medium heat until scalded. When the butter is melted, add the flour all at once and beat it with a wooden spoon until the mixture comes together and forms a dough. Cook, stirring constantly, over low heat for 2 minutes. The flour will begin to coat the bottom of the pan. Dump the hot mixture into the bowl of a food processor fitted with the steel blade. Add the eggs and pulse until the eggs are incorporated into the dough and the mixture is thick.
Spoon the mixture into a pastry bag fitted with a large plain round tip. Pipe in mounds 1 1/2 inches wide and 1-inch high onto a baking sheet lined with parchment paper. You should have about 18 puffs. With a wet finger, lightly press down the swirl at the top of each puff. (You can also use 2 spoons to scoop out the mixture and shape the puffs with damp fingers.) Bake for 20 minutes, or until lightly browned, then turn off the oven and allow them to sit for another 10 minutes, until they sound hollow when tapped on the bottom. Make a small slit in the side of each puff to allow the steam to escape. Set aside to cool.
For the chocolate sauce, place the cream and chocolate chips in a bowl set over simmering water and stir just until the chocolate melts. Add the honey and coffee and stir until smooth. Set aside.
For serving, cut each profiterole in half crosswise, fill with a small scoop of ice cream, replace the top, and drizzle with slightly warm chocolate sauce.