For the mustard sauce: Place the mustard, shallots, garlic, parsley, and lime juice in a food processor. Push pulse to process, then adjust to “on” position and drizzle in the olive oil in a slow, steady stream, until all is used up and mayonnaise is creamy thick. Transfer the mayonnaise to a small bowl and stir in sour cream, seasonings and hot sauce to your liking. Cover and refrigerate until ready to serve.
For the cheeks: Place buttermilk into a mixing bowl. Place flour, cornmeal, cracker meal, cayenne pepper and salt into a separate mixing bowl and blend with a fork or whisk. Dunk grouper cheeks into the buttermilk, then dust them with the flour mixture. Let sit for 1 minute, then drop them into the hot oil a few at a time.
To assemble: Heat the frying oil to 360°F., using a deep skillet and a clip-on thermometer. Skillet or deep-fry the breaded cheeks for 1 to 3 minutes (depending on their size), or until golden brown. Drain well and transfer fried cheeks to paper towels to drain further. Place onto platter or onto individual plates. Serve with the lime-Dijon mustard sauce.