Preheat the oven to 375 degrees F.
In a small food processor, combine the mayonnaise, piquillos, lemon zest and salt. Puree until smooth. Refrigerate until ready to use.
Line a straight-sided baking sheet with parchment paper. Sprinkle the Parmesan onto the parchment and spread thinly and evenly into an oval (or whatever shape you like).
Bake until bubbly and just beginning to brown, 9 to 10 minutes. Transfer the parchment with the crisp to a wire rack and allow to cool completely.
Serve the Parmesan crisp on a board for people to break off pieces, with the pink sauce alongside for dipping.