Avocado Jalapeno Relish: In a medium bowl, mix all relish ingredients but the lime juice. Stir gently with a fork to mix. Drizzle the lime juice over all to evenly distribute. Stir gently until fully incorporated. Cover with plastic wrap and place in the fridge until ready to assemble the burgers.
Cumin Garlic Mayo: In a small bowl, mix the mayo, cumin and garlic. Cover and refrigerate until ready to use.
Southwest Burgers: In a large bowl, crumble the beef apart and spread out across the width of the bowl. Add the onion and patty seasonings by sprinkling over the beef to evenly distribute. Mix gently with your hands, careful to not overwork the meat. Form into 6 patties.
To cook the patties, heat the grill or grill pan to medium high. Place the patties on the grates and cook for 5 minutes. Flip and grill another 4 minutes. Add the cheese slices and allow to melt, about 1 minute. (This cooking time was done on a gas grill for medium- medium well. Use a meat thermometer for your desired temperature. Your cooking time will vary if the patties have been refrigerated.).
Place the buns cut-side down on the grill until slightly toasted, about 1 minute. Keep a close watch, they can burn quickly.
To assemble, spread the mayo mixture on the bottom bun, about 1 heaping tablespoon. Place 2 or 3 pieces of lettuce as desired. Place the burgers on top, then the sliced tomato. Spoon on two generous tablespoons of relish. Add red onion if desired. Place top bun. Repeat for remaining burgers.