Cut the ends off the yuca and cut it into roughly 2 inch sections. Make sure the interior of the yuca is free of blemishes, bruises, and discoloration.
Cut a slit along the skin of each piece of yuca.
Use a knife or your fingers to get underneath the skin near the slit you made and peel away the outer layer. If the skin does not come off easily, use a knife to cut it away.
You will probably notice a small point in the center of yuca that runs down the entire length of the tuber. This is the fibrous part that we will be removing later. Cut each piece of yuca in half along this fibrous centerline.
Cut each half into thirds or quarters (in wedge-shaped pieces).
Cut off the pointy side of each wedge and discard to remove the fibrous part of the yuca.
Rinse the yuca pieces.
Put the yuca into a pot with 3 cloves of lightly crushed garlic and cover with at least 2 inches of fresh water. Season the water with salt until it tastes pleasantly seasoned. Bring to a rolling boil over high heat. Adjust the temperature of the burner to maintain a steadily rolling boil. Cook the yuca until it is starting to fray around the edges and is tender throughout. Yuca can vary greatly in cooking time. Sometimes it may only take 8 minutes but some yuca can take up to 30 minutes to soften. If the water level decreases too much, top up with more water as it cooks.
Remove yuca from the water, drain, and allow to cool for at least 10 to 15 minutes on a plate. At this point you can refrigerate the yuca and store for up to 2 days to fry at a later time.
The yuca should look frayed around the edges. If you want extra crispy yuca, you can use your fingers to break up and fray the exterior even more. The frayed bits will get extra crunchy after frying.
In a large pot, heat the oil to about 375F. Do not overfill the pot because the hot oil will bubble aggressively when you first add the yuca. (if you are frying yuca that is cold from the fridge, bring your oil up to 400F because the cold yuca will cause your fryer oil to drop in temperature significantly)
Carefully add the yuca to the oil and fry for approximately 8-10 minutes at 350F. Monitor the temperature of the oil as you fry the yuca and try to keep it at 350 the entire time. This 8-10 minute cooking time may seem a bit long but it is what will give the yuca the thick, crispy crust.
Use a spider or strainer to remove the yuca and place it on paper towels. Lightly season with salt if desired.
Serve the yuca with the aioli.