In a bowl whisk mayonnaise, ketchup, pickle relish, red onion, white vinegar & garlic powder. Cover & refrigerate until ready to use (can make up to 1 week in advance).
Press 1.2 oz (32g) of ground beef onto each flour tortilla. Make sure meat is spread thinly & evenly across tortilla right to edges. Spread ~½ teaspoon (3g) of yellow mustard per. Season with salt & pepper.
Heat a cast iron pan over high heat. Once hot, work in batches to cook tacos. Add tortilla patties, patty-side down & use a metal spatula or heavy item to smash tortilla flat onto pan.
Cook for 1 minute then use the metal spatula to scrape the patty up & flip tortilla onto skillet to warm for just a few seconds.
Remove tortillas from skilled & add to a platter. Immediately top with a slice of cheese. Repeat with remaining meat.
Return pan to heat, add the diced onion to the pan & sauté in rendered beef fat until the onions are soft & start to brown, stirring occasionally (~8 min).
Top the burgers with a spoonful of the spread, grilled onions, pickles, a slice of tomato & the shredded lettuce. Serve hot.