Rinse green beans; chop off ends. (If they're super long, cut in half.)
Mince shallots and garlic. Set aside.
Cook bacon in skillet on medium heat, stirring occasionally, until slightly underdone. (You don't want to overcook the bacon in this step because you'll cook it a bit more later on...)
Transfer bacon pieces to plate covered with paper towel. (The paper towel will absorb some of the grease.) Save for later.
Discard 2/3 of bacon fat but reserve 1/3 of fat in skillet.
Add shallots and garlic to skillet (still on medium heat). Sauté in bacon fat, stirring occasionally, until slightly browned.
Add green beans.
Season with za'atar, salt, and pepper. Cook until slightly tender, stirring occasionally, about 5 minutes.**
Chop up bacon. Add bacon back to skillet. Sauté an additional 2-3 minutes.
Pour all on serving platter; drizzle (liberally!) with extra virgin olive oil.