Heat the olive oil in a large pot over medium heat. Add the diced onion, carrot, and celery, and sauté for 8-10 minutes, stirring occasionally, until the vegetables soften and become fragrant. This creates a flavorful foundation called a mirepoix. Add the minced garlic and cook for another minute until aromatic, being careful not to burn it. I like to use extra virgin olive oil here because it adds a smooth, peppery note that complements the bright lemon flavor coming later.
Add the bay leaves, chicken breasts, and chicken stock to the pot with the sautéed vegetables. Bring to a boil over high heat, then reduce to medium-low and cover the pot. Simmer gently for 15 minutes until the chicken is cooked through and tender. Remove the pot from heat, then carefully remove the chicken breasts and bay leaves with a slotted spoon. Set the chicken aside to cool slightly on a cutting board.
While the broth simmers, shred the cooled chicken into bite-sized pieces using two forks or your fingers. Return the broth to a gentle boil and add the orzo pasta, stirring occasionally. Cook for 10 minutes until the orzo is tender but not mushy. Once the orzo is cooked, add the shredded chicken back into the pot. I find that shredding the chicken while the broth is simmering saves time and lets me work efficiently during the busiest part of cooking.
In a separate bowl, whisk together the egg yolks, freshly squeezed lemon juice, lemon zest, salt, and red pepper flakes. This mixture will create the creamy, tangy richness that defines avgolemono. Slowly temper the egg yolks by ladling 1-2 cups of the hot soup broth into the egg mixture while whisking constantly. This gradually brings the eggs up to temperature without scrambling them—a critical technique for this soup.
Remove the pot from heat and slowly pour the tempered egg-lemon mixture from Step 4 into the soup, stirring gently and constantly to distribute it evenly. Return the pot to low heat and cook for 5 minutes, stirring occasionally, until the soup thickens slightly and becomes creamy. Don't let it boil once the eggs are added, or they'll scramble and become grainy. Fresh lemon juice makes all the difference here—bottled juice won't give you the bright, clean acidity that makes this soup truly special.
Taste the soup and adjust seasoning with additional salt and cracked black pepper as needed. Stir in the fresh chopped dill just before serving for a bright, herbaceous finish. Ladle into bowls and serve immediately while hot and creamy.