Peel and cut the potatoes into 1-inch chunks, then dice the carrots, celery, and onion into 1/4-inch pieces—keeping them uniform ensures even cooking. Mince the garlic, zest both lemons, and squeeze the lemon juice into a bowl. Measure out the dried oregano, dill, salt, and pepper. This prep work takes just 10-12 minutes and ensures smooth cooking once you start.
Melt the butter in a large pot over medium heat. Add the diced onion, carrots, and celery, cooking for 4 minutes until they soften and release their aromas. Stir in the minced garlic, oregano, dill, salt, and pepper, cooking for another minute to bloom the spices—this technique deepens the flavor foundation of the entire soup.
Pour in the chicken broth and water, then add the chicken breasts and potato chunks. Add the bay leaf and bring to a boil over medium-high heat, then reduce heat to low, cover, and simmer for 20 minutes until the potatoes are fork-tender and the chicken is fully cooked. The gentle simmer ensures tender chicken and allows flavors to meld without harsh boiling.
Carefully remove the cooked chicken breasts from the pot with tongs and place them on a cutting board. Using two forks, shred the chicken into bite-sized pieces. I like to shred the chicken immediately while it's still warm—it's much easier to work with than cooled chicken. Return the shredded chicken to the pot, then stir in the fresh lemon juice and lemon zest. Taste and adjust seasoning if needed.
Ladle the hot soup into bowls and finish each serving with a sprinkle of fresh dill. I find that adding the dill as a garnish rather than cooking it in keeps its bright, herbaceous flavor intact—a small detail that makes a noticeable difference. Serve immediately with fresh lemon wedges on the side for extra brightness.