For the quick mojo aioli: Whisk together the mayonnaise, sour cream, Dijon mustard, cumin, paprika, onion powder and garlic powder. Cover and refrigerate until ready to dress the burgers.
For the burgers: Mix the ground beef, chorizo, cumin, onion powder, paprika, cayenne, salt and pepper in a large bowl, folding it over itself until thoroughly mixed. Let the meat rest 15 minutes at room temperature or for up to 4 hours refrigerated. Shape the meat into 12 balls all the same size, then lightly press them into chubby round patties.
Preheat a large cast-iron skillet over medium-high heat and add the oil. When the oil is shimmering, add the onions and sweat until translucent, 3 to 4 minutes. Add the patties on top of the onions and press the patties onto the onions using a spatula. Let cook, 3 to 4 minutes; the onions will continue to cook and caramelize in the patty juices, adding flavor to the patties. Flip the patties and cook until firm, 2 to 3 more minutes. Remove from the heat and top with the Swiss cheese.
Spread 1 tablespoon mojo aioli on the bottoms of each Hawaiian roll, then top with a patty and a generous handful of the Mini French Fries. Serve.
Mini French Fries:
Peel the potatoes, then shred them on the largest holes of a box grater. Soak in cold water to remove starch and prevent browning, 5 minutes. Strain in a colander and dry on paper towels.
Heat the oil in a Dutch oven or deep skillet over medium-high heat until the temperature reaches 375 degrees F.
Fry the potatoes in batches, moving the potatoes gently with a spider to keep them separated, until brown and crispy, about 4 minutes. Remove to a bowl, season with salt and toss to ensure all the fries are thoroughly seasoned.