Using a sharp knife, finely chop the fresh ahi tuna into 1/4-inch cubes and place in a medium chilled mixing bowl.
In a separate small bowl, lightly whisk the egg until the yolk and white are fully combined.
Add the whisked egg, almond flour, sliced green onion, grated ginger, lime zest, sea salt, and black pepper to the tuna.
Gently fold the ingredients together until just combined, then form the mixture into one large, thick patty.
Heat the avocado oil in a non-stick or cast-iron skillet over medium-high heat until shimmering.
Carefully place the tuna patty in the skillet and sear for 2 to 3 minutes per side for a perfect medium-rare finish.
Place the peppery arugula on a plate, top with the seared tuna burger, and garnish with sliced avocado and a squeeze of lime juice.