In a large stockpot or Dutch oven, heat 1 tablespoon of olive oil and 1 tablespoon of butter over medium heat. Once melted and shimmering, add 1 medium finely diced onion and 2 peeled and diced carrots. Cook for about 3-4 minutes until softened and fragrant, then stir in 4 minced garlic cloves and 1 tablespoon of finely chopped fresh rosemary, cooking for another 30 seconds until aromatic.

Pour in 10 cups of low sodium chicken broth and add 1½ teaspoons of kosher salt to the pot. Increase the heat to high and bring the broth to a rolling boil. Once boiling, stir in ¾ cup of orzo pasta, cooking for 8-10 minutes until tender, monitoring closely to prevent overcooking.

While the broth simmers, take a separate heatproof container and whisk together 3 large eggs, 2 large egg yolks, and 3 tablespoons of fresh lemon juice. Whisk vigorously until the mixture is well combined and slightly frothy.

Once the orzo is cooked, slowly ladle about 2 cups of the hot broth into the egg mixture while whisking continuously. This gradual incorporation is key to achieving a smooth, creamy consistency.

Return the pot with the remaining broth to low heat. Slowly stir in the tempered egg mixture, cooking gently for about 5 minutes while stirring frequently.

Add 2 cups of shredded chicken, ¼ cup of finely chopped fresh dill, and the zest of 1 lemon to the pot. Stir well to combine all ingredients, adjusting the thickness with additional broth if needed.

Ladle the creamy Avgolemono into bowls and garnish with extra fresh dill, lemon slices, and a sprinkle of freshly ground black pepper to taste.