Add the butter to a pot over medium heat, and once it's melted, add the onion and celery and sauté for 4-5 minutes.
Stir in the garlic and flour. Cook for about 2 minutes, breaking it up with your spoon/stirring it as you go along (this cooks the raw flour taste out).
Slowly whisk in the chicken broth until all the flour has dissolved/there's no lumps.
Stir in the cream, Worcestershire sauce, and potatoes. Crank the heat to high and bring the soup to a boil, then reduce the heat so it's simmering but not boiling rapidly (medium-low heat works with my cast iron pot & gas stove). Cover the pot with the lid slightly ajar.
Let the soup simmer for about 15-20 minutes or until the potatoes are tender and the soup has thickened up. I stir it a few times to ensure nothing is sticking and that the stove's temperature is still correct.
Turn the stove off, and stir in the cheddar gradually.
Season generously with salt & pepper. Serve and top bowls with extra cheddar and chopped chives (if using).
NOTE: You can add some diced ham or diced grilled chicken to this for extra protein and flavor if you so desire. You can also use the dried minced garlic and minced onion in place of fresh to make it easier.
