
Peel your Yukon Gold potatoes and chop them into uniform ½-inch cubes. Rinse the cubed potatoes under cold water to remove excess starch – this helps prevent the soup from becoming gummy. Set aside.
Place a large pot or Dutch oven over medium heat. Add the butter (or olive oil/butter combination). Once the butter is melted and shimmering, add the finely chopped yellow onion. Sauté for 5-7 minutes, stirring occasionally, until the onion is softened and translucent, but not browned.
Add the minced garlic to the pot and cook for another 1-2 minutes, stirring constantly, until fragrant. Be careful not to burn the garlic, as it can become bitter.
Sprinkle the all-purpose flour over the sautéed onions and garlic. Stir continuously and cook for about 1-2 minutes. This cooks out the raw flour taste and creates a roux, which will help thicken the soup.
Gradually whisk in the chicken or vegetable broth, a little at a time, ensuring you scrape the bottom of the pot to loosen any flavorful browned bits (fond). Whisking constantly prevents lumps from forming. Once all the broth is incorporated and the mixture is smooth, bring it to a simmer.
Add the rinsed and drained potato cubes to the pot. Stir well. Bring the mixture back to a gentle simmer, then reduce the heat to medium-low. Cover the pot and let it cook for 15-20 minutes, or until the potatoes are very tender and can be easily pierced with a fork. Stir occasionally to prevent sticking.
Now, it’s time to create that signature creamy texture while keeping some potato chunks for heartiness. You have two options:
Carefully ladle about half of the soup (including solids and liquid) into a standard blender. Secure the lid tightly, but remove the center cap and cover the opening with a folded kitchen towel to allow steam to escape. Blend until smooth. Pour the blended soup back into the pot with the remaining chunky soup. Warning: Blending hot liquids can be dangerous; never fill the blender more than halfway and always vent the lid.
Reduce the heat to low. Slowly pour in the whole milk (or half-and-half) and heavy cream (if using), stirring constantly. Add the fresh parsley, chives, and thyme (or dried thyme). Stir well to combine. Allow the soup to heat through gently for about 5 minutes – do not let it boil after adding the dairy, as this can cause it to curdle.
Remove the pot from the heat completely. Gradually add the shredded sharp cheddar cheese, a handful at a time, stirring continuously until each addition is fully melted and incorporated before adding the next. Adding cheese off the heat prevents it from becoming grainy or seizing.
Taste the soup and season generously with salt, freshly ground black pepper, and a pinch of cayenne pepper or smoked paprika if desired. Remember that the cheese adds saltiness, so season gradually.
Ladle the hot, creamy soup into bowls. Garnish generously with your chosen toppings like crumbled bacon, extra cheese, sour cream, fresh chives, or croutons. Enjoy immediately!