4 ounces feta cheese, crumbled
3 1/2 teaspoons kosher salt
1 3 1/2- to 4-pound whole chicken
1 to 2 tablespoons cracked black pepper, to taste
2 tablespoons dried Greek oregano
2 large lemons
1/4 cup olive oil, more as needed
1 large bunch arugula or other sturdy salad greens, for serving
The day before serving, combine 2 ounces feta, 2 teaspoons salt and 4 cups water in a blender and blend until smooth. Put chicken in an extra-large resealable plastic bag or a container large enough to submerge chicken, and cover with the feta brine. Refrigerate at least 8 hours or overnight.
Before cooking, remove chicken from brine and transfer to a towel-lined tray. (Discard brine.) Pat chicken dry with paper towels and allow to come to room temperature for 1 hour.
In a small mixing bowl, combine remaining 1 1/2 teaspoons salt, the pepper, the oregano and the zest of the lemons (about 1 tablespoon). Liberally cover chicken in herb mix and gently massage entire bird. Halve lemons and place 3 halves in cavity (save remaining half for serving). Using kitchen twine, tie legs together.
Heat oven to 450 degrees. Place a large ovenproof skillet over high heat. Add oil and heat until it just smokes. Place chicken, breast-side up, in pan. Transfer entire pan to oven. Cook, basting once or twice, until juices run clear when chicken is pierced with a knife, 50 to 60 minutes.
Remove pan from oven, then stir remaining crumbled feta into juices in pan and stir well. Let chicken rest for 10 minutes in the pan before slicing and serving on a bed of greens, with feta-laced pan juices on top, drizzled with a little lemon juice from the reserved lemon half.