Directions for the Cumin Mayo:
Combine the egg yolks, mustard, cumin, salt and lemon juice in a food processor. Blend until mixed well and slowly stream in oil to create an emulsion. Once all the oil is added, finely grate the garlic and pulse a couple of times to incorporate. Set aside.
Directions for the Burgers:
Gently form meat into four 8-ounce patties of even thickness. They should be slightly wider in diameter than the buns, ideally about 4 1/2 inches.
Sprinkle both sides of each patty with a pinch of salt and grill over medium-hot coals for 3 minutes per side. Place patties on a cooler part of grill for an additional 3 to 4 minutes, or until medium-rare. Remove from heat to a warm place. As burgers are resting, top each with crumbled feta cheese. Meanwhile, toast buns on their outsides over the grill so you get a nice crunchy exterior and a soft, warm center. Garnish burgers with red onions, sliced cucumbers, fresh arugula and cumin mayo.