Set a large Dutch oven or soup pot on the stove over medium heat.

Add 2 tablespoons of the butter to the pot and let it melt.

Add the onion, carrots, celery, and 1/2 teaspoon of the salt to the pot.

Cook the vegetables for 6 to 8 minutes, stirring a few times, until the onion is soft and the carrots and celery start to lose their raw crunch.

Add the garlic and dried thyme to the pot.

Cook for 30 seconds, stirring, until the garlic smells fragrant.

Sprinkle 3 tablespoons of the flour over the vegetables in the pot.

Stir for 1 minute so the flour coats the vegetables and no dry patches remain.

Pour the chicken broth into the pot a little at a time, stirring as you pour so the flour blends in smoothly.

Pour 1/2 cup of the milk into the pot and stir well.

Increase the heat to medium-high and bring the soup to a gentle simmer.

Add the shredded chicken and the frozen peas to the pot.