To make the mayonnaise, in a food processor combine the whole egg, yolk, lime juice, mustard, salt, and cayenne. Blend well and, with the motor running, drizzle in the olive oil very slowly until the sauce thickens. Transfer to a small bowl and stir in the cracked pepper. Cover and set aside, refrigerated, until ready to use or for up to one week.

Place the yucca in a large sauce pan and cover with cold water. Bring up to a boil, then reduce the heat so that the water is simmering and cook for 20 to 25 minutes, or until fork tender. Check individual pieces for doneness; some pieces may cook faster than others. Drain in a colander and, when cool enough to handle, cut into quarters lengthwise and remove and discard the fibrous cores. Slice very thinly and place on a layer of paper towels. Cover with another layer of paper towels and pat dry. In a large heavy sauce pan or deepfat fryer, heat the oil to 375 degrees. Deep-fry the yucca chips in several batches until golden, then drain on paper towels. Increase the heat under the fryer so that the oil comes to 390 degrees and, again in several batches, deep-fry the chips until they are deep golden and slightly puffed. Drain again briefly on paper towels and sprinkle with the sea salt. Mound the chips around the edges of a large platter and place the bowl of lime pepper mayonnaise in the center. Scatter a few lime wedges among the chips.

*RAW EGG WARNING

Food Network Kitchens suggest caution in consuming raw and lightly-cooked eggs due to the slight risk of Salmonella or other food-borne illness. To reduce this risk, we recommend you use only fresh, properly-refrigerated, clean, grade A or AA eggs with intact shells, and avoid contact between the yolks or whites and the shell.