Cook bacon until crispy, let bacon drain, but reserve bacon grease.
In a medium mixing bowl, mix ground beef, yellow mustard, coconut aminos, salt, pepper, and garlic powder well with your hands. Make 4 burgers, place on a plate, and set aside.
In a large non-stick pan, pour 1 tablespoon of olive oil and three tablespoons of the reserved bacon grease to medium high heat and cook mushroom slices until cooked through and seared. Set aside mushroom slices in a bowl.
In the same pan on medium high heat, add 1 tablespoon olive oil and cook the onion slices, until they sear and then start to soften. Season with salt and pepper. Turn heat down to medium low, cover pan, and cook 10-12 minutes until onions start to get brown and caramelized. Remove cover and turn off heat when onions are desired doneness.
In a small mixing bowl fold the cherry tomato pieces, chopped basil leaves, remaining tablespoon of olive oil, and vinegar. Season with salt and pepper and set aside.
Heat grill up to 500 degrees and grill burgers until desired doneness, about 2-3 minutes per side. Lay cheese slices atop each burger to melt for the final minute of cooking. If cooking stovetop, heat a flat bottomed nonstick sauté pan to medium high heat and cook burgers through, about 2-3 minutes per side for medium. Add cheese atop each burger to melt in the final minute of cooking. Plate burgers by laying down a butter lettuce leaf, the burger with cheese, lay two bacon slices, then onions, mushrooms, and tomato basil mixture. Garnish with pickle slices and top with final butter lettuce leaf. Repeat plating for remaining burgers and serve.