Step 1

Prepare the following, adding each to the same medium bowl as you complete it: Peel and dice 2 medium carrots (about 1 cup). Dice 1 medium yellow onion (about 1 1/2 cups) and 1 medium celery stalk (about 1/2 cup). Finely chop 3 garlic cloves.

Step 2

Prepare the following, adding each to the same second medium bowl as you complete it: Peel and dice 1 1/2 pounds russet potatoes (about 3 1/2 cups). Dice 7 to 8 ounces cooked ham if needed (about 1 1/2 cups).

Step 3

Melt 5 tablespoons unsalted butter in a Dutch oven or medium pot over medium heat. Add the carrot mixture, 1/2 teaspoon dried thyme or 2 fresh thyme sprigs, 1/2 teaspoon of the kosher salt, and 1/4 teaspoon black pepper. Cook, stirring occasionally, until the onion is softened and translucent, about 5 minutes.

Step 4

Add the ham, potatoes, and remaining 1 teaspoon kosher salt, 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 3 cups low-sodium chicken broth and 2 cups whole or 2% milk. Increase the heat to medium-high and bring to a lively simmer, stirring occasionally (do not let boil).

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 very tender and the soup thickens slightly, about 20 minutes. Taste and season with more kosher salt and black pepper as needed. Remove the thyme sprigs if needed before serving.