Chop 1/2 white onion, 1 yellow squash, 3 carrots, and 2 celery stalks. Mince 4 cloves of garlic. Pound 2 boneless skinless chicken breasts to an even thickness to make them more tender and help them cook through quicker. Season both sides with salt and a dash of pepper.
Bring a sturdy bottom pot to medium-high heat. Melt in 2 tablespoons butter, add the chopped onion and yellow squash, and cook for 4-5 minutes until tender. Add the minced garlic and cook for one more minute. Transfer the mixture to a blender with 5 cups chicken broth and blend until completely smooth.
Add 2 tablespoons light olive oil to the same pot over medium-high heat. Add the seasoned chicken breasts and brown on both sides until golden, about 3-4 minutes per side. The chicken doesn't need to be cooked through yet – you're just creating that flavorful crust.
Move the chicken to one side in the pan and carefully pour about 1/2 cup of the blended stock into the pot. Scrape the bottom with a wooden spoon to loosen the chicken bits and deglaze the pot. Move the chicken to the other side of the pot and repeat with another 1/2 cup of stock. Pour in the remaining blended stock. Add the chopped carrots, celery, 2 teaspoons dill, 1/2 teaspoon thyme, 1/2 teaspoon oregano, and 1 teaspoon salt. Cover and simmer for 10 minutes.
Add 3/4 cup orzo pasta to the pot. Cover and simmer for an additional 8 minutes for small orzo or 10 minutes for large orzo, stirring occasionally to prevent sticking.
Remove the chicken breasts from the pot and place on a cutting board. Add the spinach, 2 tablespoons lemon juice, and 2 tablespoons lemon zest to the soup. Allow to simmer while you shred the chicken with two forks. Return the shredded chicken to the pot, stir everything together, and serve.