Preheat oven to 200 degrees C. Line a baking tray with foil.
Cook mint leaves in a saucepan of boiling water for about 10 seconds. Transfer mint leaves to a bowl of ice water; soak for 30 seconds, drain and squeeze dry.
Combine blanched mint with garlic, olive oil, breadcrumbs, salt, black pepper and cayenne pepper in a food processor or blender. Blend for 20 to 30 seconds until fine and crumbly.
Transfer mint mixture to a large bowl; stir in cheese, set aside.
Combine 1/4 cup Dijon mustard and 2 teaspoons honey in a small bowl, set aside.
Combine extra-virgin olive oil, rice vinegar, extra honey, extra Dijon mustard, salt and black pepper in a jar with a lid. Shake vinaigrette vigorously until combined, about 30 seconds. Set vinaigrette aside.
Slice 2-3cm slits between each bone of the lamb racks to ensure the meat roasts evenly.
Season each rack with salt and black pepper on all sides. Heat vegetable oil in a large frying pan over high heat. Brown each lamb rack for 2 to 3 minutes on each side.
Transfer lamb racks to the prepared baking tray. Brush each rack with mustard and honey mixture. Sprinkle mint mixture over the top and sides of each rack and press down firmly.
Bake about 20 minutes or until browned and medium rare in the center. An instant-read thermometer inserted into the center should read 52 to 54 degrees C. Remove from oven and allow lamb to rest for 10 minutes before serving, drizzled with honey mustard vinaigrette.