If the caramel dust begins to clump, regrind it in the food processor.
Heat 2 tablespoons water and the sugar in a small saucepan over medium-high heat, stirring until sugar has dissolved. Continue to cook, without stirring, until mixture comes to a boil, washing down sides of pan with a wet pastry brush two or three times to prevent crystals from forming. Let boil, gently swirling pan occasionally, until light amber.
Remove from heat. Add butter and salt; stir until combined. Immediately pour onto a rimmed baking sheet lined with parchment paper. Let cool completely. Break hardened caramel into pieces; finely grind in a food processor. Caramel dust can be stored in an airtight container in a dry place at room temperature up to 2 days.