Heat butter or oil in a large pot or Dutch oven over medium heat.
Add onion, celery, and carrots, and sauté until onions are translucent.
Add the minced garlic, thyme, salt, pepper, and bay leaves. Stir. Then add the potatoes, chicken, broth, and water. Cover and bring to a simmer.
Add potatoes, chicken, chicken broth, and water.
Simmer on medium-low for 20-25 minutes, until the potatoes are fork-tender.
Remove the bay leaves. In a small bowl, whisk together the flour and heavy cream until smooth. Slowly pour into the soup, stirring constantly to prevent lumps.
Whisk the flour and heavy cream in a small bowl. Slowly pour the mixture into the soup, stirring to prevent lumps.
Stir in the frozen peas and corn, then return the soup to a gentle simmer. It will thicken as it cooks.
When you’re ready to serve, ladle the soup into bowls and serve with your choice of bread.