Best-Ever Lamb Burger

In a medium bowl, stir to combine yogurt, feta, mint, and lemon juice. Season with salt and pepper. Divide ground lamb into 4 equally sized patties. Make an indent with your thumb in the center of each patty, and season both sides generously with salt and pepper. Heat a large cast iron skillet over medium-high heat. Add burgers and cook  until crisp on the outside and still slightly pink in the center, 6 minutes per side for medium. Spread each top and bottom bun with yogurt sauce. Top with the patty, red onion, arugula, and top bun.