Brine the chicken. A day before you plan to roast the chicken, combine the brine from the feta container (about 1 cup) along with 2 teaspoons salt, and Greek oregano in a blender. Crumble in half the cheese, about 4 ounces. Pulse, then puree. With the blender running, stream in water. Add the brine to a large resealable bag or container, then add the chicken, squeezing out the air to coat the chicken in brine as thoroughly as possible. Refrigerate for 1 day.
Get ready. Preheat the oven to 400°F. Remove the chicken and discard the brine. Use paper towels to pat the chicken dry inside and out. Remove as much moisture as you can. Allow it to sit at room temperature while the oven preheats.
Make the Lemon-Garlic Rub. Combine the salt, black pepper, oregano, thyme in one bowl. In a second bowl, combine olive oil, grated garlic, and lemon zest in a bowl, stir to make a paste.
Season the chicken. Film a rimmed baking sheet or a roasting pan with olive oil. Season the cavity of the chicken with ⅓ of the oregano mixture and place it on the prepared pan. Loosen the skin from the breast meat and the legs by inserting your fingers between the skin and the flesh. Rub half of the remaining oregano mixture into the garlic-oil mixture and rub it between the skin and flesh of the chicken. Sprinkle the remaining dry seasoning all over the chicken.
Roast the chicken. Move pan to the oven and roast, until the chicken registers 165°F in the thickest part of the breast, about 1 hour.
Rest the chicken. For at least 10 minutes and then carve into pieces. Serve topped with crumbled feta and fresh parsley, with lemon wedges on the side.
