How to Make It
Heat oven to 375° F. Line a baking sheet with parchment.
Spoon the Parmesan onto the baking sheet in 8 mounds (about 2 tablespoons each), spaced 1 inch apart. Flatten the mounds gently with your fingers, then season with ½ teaspoon pepper. Bake, rotating the baking sheet halfway through, until golden and bubbly, 10 to 12 minutes. Let cool for 5 minutes, then remove from the parchment.
Meanwhile, heat the oil in a large pot over medium-high heat. Add the onion and ¼ teaspoon each salt and pepper and cook, stirring often, until beginning to soften, 5 to 7 minutes.
Add the broth, thyme, and Parmesan rind and bring to a boil. Reduce heat and simmer, stirring occasionally, until the liquid is slightly reduced and the Parmesan rind is very soft, 10 to 15 minutes; add the peas during the last 3 minutes of cooking. Remove the thyme sprigs and Parmesan rind.
In batches, puree the mixture in a blender until smooth. Serve drizzled with the yogurt, sprinkled with the thyme leaves, and topped with the Parmesan crisps.