Special equipment: an immersion blender; a deep-frying thermometer
For the aioli: Place the garlic, egg yolk, lemon juice, mustard and water into the cup of an immersion blender. Pour the avocado oil on top of the other ingredients and wait a few moments for the oil to separate from the ingredients beneath it. Gently nestle the blade of the immersion blender into the egg yolk at the bottom of the cup. Turn on the blender and blend until the mixture is fully emulsified, about 1 minute. Add salt to taste. Cover and refrigerate until ready to serve.
For the frites: Fit a large Dutch oven with a deep-frying thermometer and fill with 3 inches of canola oil. Heat the oil to 325 degrees F.
Dry the potatoes thoroughly with kitchen towels. Working in batches to avoid crowding the pot, slide the potatoes into the hot oil and fry until softened but not colored, 3 to 4 minutes. Using a slotted spoon or metal spider, remove to a paper-towel-lined plate.
Raise the oil temperature to 350 degrees F. Again working in batches, return the potatoes to the oil and fry until deep golden brown, another 3 to 4 minutes. Drain on a paper-towel-lined tray and season with salt.
Serve immediately with aioli.
Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.