Step 1

Prepare the following vegetables, adding them all to the same bowl: Dice 1 medium yellow onion and 3 medium celery stalks, peel and cut 2 medium carrots into 1/2-inch thick rounds, and mince 2 garlic cloves.

Step 2

Season 2 pounds chicken breasts all over with 1 teaspoon of the kosher salt and 1/4 teaspoon black pepper.

Step 3

Melt 2 tablespoons unsalted butter in a Dutch oven or large pot over medium heat. Add the onion mixture and the remaining 1/2 teaspoon kosher salt. Cook, stirring occasionally, until softened, about 5 minutes. Add 1/4 cup all-purpose flour, stir to coat the vegetables, and cook for 1 minute.

Step 4

Pour in 1 cup of the chicken broth and stir with a wooden spoon, scraping the bottom of the pot, until no lumps from the flour remain.

Step 5

Push the vegetables to the sides of the pot and add the chicken breasts to the empty space, arranging them in a single layer. Add 1 teaspoon dried thyme and 1 bay leaf, then pour in the remaining 5 cups chicken broth. Cover and bring to a boil over medium-high heat. Uncover, reduce the heat, and simmer until the chicken is cooked through and an instant-read thermometer inserted into the thickest part registers 165°F, 8 to 12 minutes.

Step 6

Remove and discard the bay leaf. Using tongs, transfer the chicken to a clean cutting board and let cool slightly. Meanwhile, add 2 cups egg noodles to the soup and cook, stirring occasionally, until al dente, about 5 minutes.

Step 7

Once cool enough to handle, shred the chicken with 2 forks or cut it into bite-sized pieces, then return it to the soup. Stir in 1 cup whole milk or half-and-half.