Mix the veal, beef, and lamb until evenly combined but not overmixed. Form into four patties and place aside until later.
Using the gas stovetop, char the Poblano until all sides are black. Place in a container with a lid and let steam for a few minutes to soften the skin.
Using paper towels, remove the charred skin, seeds and stem from the Poblano flesh. With a stick bender, blend the Poblano flesh with one cup of aioli, then set aside.
In another container, stick blend another cup of aioli with the preserved lemon and save for later.
Using a 12-inch skillet and some oil sauté the Japanese eggplant until browned and soft.
Add the red onions and bell peppers and cook for another three minutes. Next add the garlic and tomatoes to the pan and cook for three minutes more.
Lastly add the oregano, parsley, red wine vinegar, and a pinch of salt and cook for one more minute. Place in a bowl and save for later.
Cut the zucchini into french-fry sticks, discarding the core, and lightly salt them. Next toss them with some flour and set aside.
Make the tempura batter by whisking together in a bowl, two cups of flour, cornstarch, baking powder, salt, egg, and cold seltzer.
Heat two quarts of oil to 350 degrees Fahrenheit in a pot. Dredge the floured zucchini in the tempura batter and place in the oil to fry for around three to four minutes or until golden brown. Remove from the fryer, season with salt, and drain on a paper towel.
Heat a large pan, preferable cast-iron, over a medium high flame. Toast the buns and set aside. Season the outside of the patties with salt and pepper and cook the burger for around three minutes aside or until they are at your desired doneness. Remove from the pan.
Lightly dress the arugula with the red wine vinegar, extra virgin olive oil, and a pinch of salt and pepper.
To build the burger, start from the bottom up: bun, Poblano aioli, eggplant relish, burger, arugula, Poblano aioli, and bun. Serve with the fried zucchini and the preserved lemon aioli.