This Greek soup gets its name, avgolemono, from the egg-lemon mixture used to thicken the broth. Some versions are simply broth that’s thickened and seasoned, while others are more substantial and include rice and chicken, as we’ve done here. To boost the flavor of store-bought chicken broth, we poach bone-in chicken breasts in it, then shred the meat and add it to the soup just before serving. Grated carrots lend sweetness and color, while lemon zest deepens the citrus notes. To prevent the eggs from curdling, keep these tips in mind: Temper the eggs first by slowly adding a small amount of the hot broth to the bowl before whisking the mixture into the pan. And after adding the mixture, don’t let the soup reach a boil or even a simmer.