In a large bowl add the carrot, celery, onion, thyme, bay leaf, peppercorn and salt and mix well. Add the pigs ears and coat with the mixture.
Divide ears among 2 large vacuum bags and add two cups of chicken stock to each. Vacuum seal and put in refrigerator for two or three days to cure the ears.
Remove the ears from the bags and rinse well, discarding the cure. Put the ears in fresh bags with a tablespoon of neutral oil and cook sous vide at 176°F (80°C) for 20 hours. (At this point you can refrigerate them in the bags for several weeks or freeze them for longer storage.)
In a blender mix the egg yolks, peppers and 4 tablespoons of lime juice. Drizzle in the oil while blending until a thick mayonnaise forms. Salt to taste.
Remove the still warm ears from the bags, place on a rack over a sheet pan to drain and cool, about 30 minutes, then cut them into 1/2" strips. In a small bowl, mix together the spices and sugar. Spoon the spice mix into a clean sugar shaker.
Heat 3-inches of oil to 350 degrees F. in a countertop electric fryer, cast-iron skillet, or deep pot. Using a slotted spoon, carefully lower the pig ear strips into the hot oil, in batches to avoid over crowding. Fry, stirring occasionally, until the strips begin to brown, about 4 to 5 minutes. Remove them from the oil and transfer directly to a large stainless steel mixing bowl without draining on paper towels; the residual oil will help the spices adhere to the pig ears. While hot, toss the fried pig ears with the salt, and shake the spice mix in as you toss to evenly coat; not all of the spice mix may be needed. Serve with lime wedges and Chili-Lime Mayonnaise.