Combine the piment d'Espelette, vinegar, sugar, and water in a medium saucepan and bring to a boil, dissolving sugar. Let cool to room temperature.
Bring a large kettle of salted water to a boil. Add cauliflower and blanch until crisp-tender, about 4 to 5 minutes. Drain.
Transfer cauliflower to canning jars and pour pickling liquid over the top. Let cool to room temperature, then cover and refrigerate.