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, 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. In a separate mixing bowl place flour, cornmeal, cracker meal, cayenne pepper, and salt. 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 2 to 3 minutes (depending on their size), or until golden brown. Transfer fried cheeks to paper towel-lined plate to drain. Place onto individual plates for first course or main course and serve with the lime-Dijon mustard sauce.