Step 1

Prepare the following vegetables, adding them each to the same medium bowl as you complete it: Dice 1 medium yellow onion (about 1 1/2 cups). Peel and halve 2 medium carrots lengthwise, then cut crosswise into 1/2-inch pieces (about 1 cup). Cut 2 medium celery stalks crosswise into 1/4-inch pieces (about 1 cup). Finely chop 3 garlic cloves.

Step 2

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

Step 3

Heat 2 tablespoons olive oil in a Dutch oven over medium heat until shimmering. Add the onion mixture, 3/4 teaspoon dried thyme, 1 bay leaf, and the remaining 1 teaspoon kosher salt. Cook, stirring occasionally, until the onion is softened and translucent, about 5 minutes. Meanwhile, cut 1 1/2 pounds Yukon Gold potatoes into 1-inch cubes (about 3 1/2 cups, no need to peel).

Step 4

Add the potatoes to the pot and stir to combine. Sprinkle with 1/3 cup all-purpose flour and cook, stirring constantly, for 1 minute to cook the floury taste out. While stirring constantly, pour in 1 (32-ounce) box low-sodium chicken broth and 2 cups whole or 2% milk. Add the chicken in a single layer. Increase the heat to medium-high and bring to a lively simmer, stirring occasionally.

Step 5

Reduce the heat as needed to maintain a gentle simmer. Cook, stirring and scraping the bottom of the pot occasionally, until the potatoes are tender, the chicken is cooked through, and an instant-read thermometer inserted into the thickest part of the chicken registers at least 165°F, about 10 minutes for thighs or 12 to 18 minutes for breasts.

Step 6

Remove the pot from the heat. Using tongs, transfer the chicken to a clean cutting board and shred into bite-size pieces.

Step 7

Remove and discard the bay leaf. Return the chicken to the soup. Taste and season with more kosher salt and black pepper as needed.