For the aioli: Combine the eggs yolks,mustard and garlic in the bowl of a food processor. Start the machine and add 1/2 cup of the oil in a fine stream. Add the lemon juice,salt and pepper, then add the remaining oil and process until thick and smooth. Refrigerate until needed.
For croquettes: Cook the rice in 1 cup boiling salted water for 20 minutes or until done. Add the butter while the rice is still hot. Add the shrimp,onion,lemon juice and House Seasoning to taste. Stir in the flour and eggs. Refrigerate this mixture for 2 hours.
Shape the rice mixture into patties and coat with bread or cracker crumbs. Heat the oil in a 10 inch cast iron skillet. Oil should be hot but not smoking. Fry the croquettes over medium-high heat until nice and golden brown on both sides. Drain on paper towels. Serve with Aioli.