Melt butter (2 tablespoons) in a large pot over medium-high heat.
Add the carrot, celery, and onion. Sauté over medium high heat until softened and browned, about 5 minutes.
Add the chicken broth (6 cups) and chicken breasts (2), along with some kosher salt (about 1 teaspoon) and pepper (about 1/2 teaspoon). Bring to a boil.
Cover and simmer on low heat for 15-20 minutes, or until chicken is fully cooked (this will depend on how thick the breasts are).
Remove the chicken and place on a cutting board. Add the dry pasta to the soup. Stir, and simmer until cooked through (this will depend on what kind of pasta you are using- about 6-8 minutes).
Meanwhile, shred the chicken with two forks. I like to shred it into larger pieces. Add back to the pot.
Once the pasta is cooked through, turn off the heat and stir in the lemon juice and dill. Season to taste with more salt and pepper if needed and serve.
Notes
For a gluten-free option: Use gluten-free pasta (such as chickpea) or substitute the pasta with 3/4 cup rice. If you use rice, add it when you add the chicken so it fully cooks. I recommend white rice, since it cooks faster than brown.
For a dairy-free option: Use ghee or olive oil instead of butter to brown the vegetables.
To make ahead and freeze: Do everything as directed except don't the pasta. Freeze in an airtight container for up to 6 months. When you are ready to serve, defrost on the stovetop and add the pasta to cook. Otherwise, it will turn very mushy.
For an even faster version, use already cooked shredded chicken, such as rotisserie, and skip the poaching step.
To save even more time, you can use already cooked pasta (such as ready pasta) or leftover cooked rice. Just decrease the amount of chicken broth to 4 cups.
The provided nutrition information does not include any added sodium from seasoning to taste, any optional ingredients, and it does not take brands into account. Feel free to calculate it yourself using this calculator or by adding the recipe to Yummly.