I adopted a tip from Bon Appetit here to ensure the fries cook up nice and crisp (as eggplant has a tendency to get soggy quickly). The key is to soak the eggplant slices in cold water for at least 2 hours before frying: the ice water helps them absorb liquid and become quite cool so when they hit the hot oil, the exterior crisps up leaving the interior nice and creamy but not at all greasy. We ended up having leftover aioli that we used on sandwiches the next day, and it keeps in the fridge just fine for a few weeks.
Make the aioli: Mash garlic and salt in small bowl until paste forms. Whisk in the mayonnaise, lemon juice, and harissa. Taste and adjust seasoning with additional harissa or salt and pepper, as desired. Store covered and refrigerated for up to 2 weeks.
Make the fries: Cut the eggplant crosswise into 1/2 -inch rounds, then cut each round further into 1/2 -3/4 inch thick strips (or any fry size you happen to like – just make sure they’re uniform). Place eggplant strips in a large bowl filled with enough ice water to cover them (about 2-3 cups water and plenty of ice). Place a plate on top of eggplant strips to weigh them down — you want them totally submerged. Cover and chill for at least 2 hours and up to overnight.
Meanwhile whisk both flours, cornmeal, salt, pepper, oregano, paprika and lemon zest in a medium bowl. In a separate small bowl, whisk eggs.
Pour oil into a large deep pot or wok suitable for frying to a depth of 1 1/2 – 2 inches. Attach a thermometer to the side of the pot and heat oil over medium heat to 325°.
Drain eggplant sticks from the water and pat dry with a paper towel or clean towel. Working in small batches, submerge the eggplant sticks in the egg mixture then toss well in flour mixture to coat. Fry them, turning occasionally so they cook uniformly, until golden brown, about 3-4 minutes. Transfer to a paper towel-lined plate to drain. Serve immediately with harissa aioli.