Melt the butter in a large Dutch oven over medium heat. Stir in the leeks, salt, and pepper. Cook, stirring occasionally, until the leeks are tender but still hold their shape, about 15 to 20 minutes.

Stir in the garlic and thyme and cook until fragrant.

Stir in the flour and cook for 1 minute to coat the vegetables and remove the raw flour taste.

Slowly whisk in the broth and water, scraping any browned bits from the bottom of the pot. Add the bay leaves and potatoes and increase the heat to medium-high until the liquid reaches a simmer.

Reduce the heat to low, cover, and simmer gently until the potatoes are nearly tender, about 10 to 15 minutes.

Remove the pot from the heat and let the soup sit, covered, for 10 to 15 minutes—this allows the potatoes to finish cooking through without becoming mushy or waterlogged.

Discard the bay leaves and season with additional salt and pepper to taste. Serve hot with crusty bread.