How to Make It
In a medium saucepan, heat the olive oil until shimmering. Add the onion, ginger, coriander and crushed red pepper and cook over moderately high heat, stirring, until softened, about 3 minutes. Stir in the rhubarb, cherries, vinegar and sugar and bring to a boil. Simmer over moderately high heat, stirring occasionally, until the rhubarb starts to break down and the chutney thickens slightly, about 8 minutes. Season the chutney with salt and let cool completely.
Preheat the oven to 350° and line a baking sheet with a silicone mat or parchment paper. In a medium bowl, whisk together the Pecorino and Parmigiano cheeses. Working in batches, spoon 1-tablespoon mounds of the cheese onto the prepared baking sheet, spacing them 2 1/2 inches apart. Use your fingers to flatten the mounds slightly, then season each mound with pepper. Bake for about 13 minutes, until the crisps are golden brown and lacy. Using a spatula, transfer the crisps to a rack to cool and harden. Serve the crisps with the rhubarb-cherry chutney.