In a mixing bowl, stir together orange and lime juices, zests, garlic, cumin, oregano, kosher salt, pepper, and cilantro. Make a "panade" by adding torn bread pieces to the sauce. Stir to combine and let stand 5 minutes. Mash the soaked bread with the back of a spoon until the mixture is a paste-like consistency. Mix in ground beef until the panade is fully distributed (for tender burgers, don't over-mix).

Divide meat into 6-ounce portions and shape into 1/2-inch thick patties. (I use a burger press). Use your knuckles to make a slight indentation in the center of each patty for even cooking.

Heat grill over high heat. Oil grates or line with a non-toxic, nonstick grill mat.

Sear burgers over direct heat, about 3 minutes per side. Move burgers to indirect heat and continue cooking until desired doneness is reached, closing lid and topping with cheese to melt during the last few minutes of cooking.

Brush onion slices with oil. Grill onions over medium heat until soft and caramelized, about 5 minutes per side. Lightly brush insides of buns with oil and grill until toasted, about 1 minute.

Whisk together mayonnaise, sour cream, lime zest, garlic, and tequila. Cover and refrigerate until ready to serve.

Place grilled burgers on toasted buns and top with onions, sliced avocado, and aioli.