Heat the oven to 450°F with the rack in the middle position.
While the oven is heating up, pat your chicken pieces dry with a paper towel. Next, sprinkle kosher salt liberally (about 2 teaspoons) on both sides of the chicken pieces.
Cut one lemon in half crosswise. Then, cut one of the lemon halves in half lengthwise before slicing it into thin half-moons. Set aside the lemon slices.
Then, cut the second lemon in half crosswise and juice the remaining three lemon halves. Measure out 3 tablespoons of the lemon juice and set it aside.
Heat a 12-inch oven-safe heavy bottomed skillet over medium high heat. When the pan is hot, add the oil to the pan. Then, sear the chicken pieces skin-side down in the hot pan until nicely browned and crispy, about 5 minutes. While the skin is crisping, add freshly ground black pepper to the meaty side.
Once the skin is golden brown, flip the pieces over and cook for 2 minutes more. Transfer the chicken to a clean plate and turn off the heat.
Spoon off the excess fat in the pan, leaving just enough oil to coat the bottom of the skillet. Add the minced garlic to the pan and stir it around so it gets fragrant but not burned. Then, pour the broth and reserved fresh lemon juice in the pan.
Turn the heat on medium and bring the sauce to a simmer. Scrape up any browned bits on the bottom of the pan.
Taste for seasoning and add salt and pepper as needed. Then, tuck in the thyme sprigs and lemon slices. Arrange the chicken pieces back in the pan, skin-side up.
Transfer the pan to the hot oven. Roast the chicken for 15 to 20 minutes or until the internal temperature of the chicken reaches 175°F to 185°F.
Garnish the chicken with a shower of minced Italian parsley, and dig in!