In a food processor, add the parsley, garlic, grated parmesan, and toast quarters. Pulse until you achieve a coarse breadcrumb texture.
Spread the herb breadcrumbs into a flat, large baking dish and set it aside.
Preheat your oven to 150°C (around 300°F).
Prep the lamb rack by removing any membrane and scoring the fat side with a knife. Season it with salt and pepper.
In a cast-iron skillet, heat oil over high heat. Sear the lamb rack starting with the fat side down for two minutes. Then, proceed to sear the other sides until they are nicely browned.
Remove the lamb rack from the skillet. Brush the fat side with Dijon mustard, then press this side into the herby breadcrumbs.
Brush the other side of the lamb rack with mustard and rotate it in the herb crust, making sure each side is well coated with the breadcrumbs.
Place the lamb on a wire rack inside a baking dish. If you have an oven-safe probe, insert it into the thickest part of the lamb.
Bake until the lamb reaches an internal temperature of 60°C (about 140°F). The cooking time may vary depending on the oven and the size of the lamb rack, but it usually takes about 25-30 minutes for medium-rare.
Once cooked, let the lamb rest for at least 10 minutes before serving.