Combine eggs, green onion, and the chicken broth in a 3 cup earthenware pot or a small, heavy bottomed stainless steel saucepan.
Mix it well with a fork or whisk.
Cover with dome-shaped heat-safe ceramic or stainless-steel bowl that fits over the pot.
Set it over medium-low and cook for about 12 to 13 minutes (about 8 to 10 minutes if using stainless steel saucepan), until steam comes out and steamy liquid begins to drip down the sides. The eggs will smell nutty.
Carefully remove the lid and drizzle on the sesame oil and serve right away with rice.
