In large dish, combine parsley, thyme, marjoram or oregano, ground sumac, sesame seeds, salt, pepper, 2 cloves chopped garlic and 2 tablespoons olive oil. Turn chicken in za’atar spice blend to coat.
Heat a skillet over medium-high heat with about 1/4 cup olive oil, 4 turns of the pan. Add potatoes and salt them; brown 10-12 minutes to golden. Add the green beans, chili flakes and remaining garlic; turn and toss. Cover and cook 7-8 minutes more, turning occasionally; keep warm.
Heat another skillet over medium-high heat, brown a halved lemon in olive oil; remove and reserve. Add chicken and brown on both sides; add stock and partially cover pan. Cook chicken through 7-8 minutes then douse with juice from reserved lemon.
Serve the chicken over or alongside potatoes and beans.