Preheat the outdoor grill to medium-high. Dice onions, mince garlic, and cut avocado into thick slices.

Toss onions and garlic into a large bowl with parsley, beef, mustard, egg, almond flour, sea salt, and pepper. Mix together until thoroughly combined; set aside.

Divide meat into 6 even pieces, then split those pieces in half. Form thin hamburger patties and add a few slices of avocado to half of the patties. Avocado slices may be chopped further to fit if needed. Top off with a second patty and seal the edges to keep the avocado inside while cooking.

Place each patty on a grill and cook for 4-6 minutes per side, checking for desired doneness.

Meanwhile, slice tomatoes and cucumbers; set aside. Slice or cube cantaloupe.

Remove burgers from the grill. Toast hamburger buns, if desired.

Add burgers to buns; top with tomatoes, cucumbers, and lettuce. Serve cantaloupe on the side.