Melt butter and olive oil in a large pot over medium-high heat. Saute leeks, onion, garlic, bay leaves, and coriander in hot butter and oil until softened and translucent, about 7 minutes. Add potatoes and chicken bouillon to the pot and pour enough chicken stock over the top to cover vegetables. Bring to a boil, reduce heat to medium-low, and simmer, stirring occasionally, until vegetables are tender, about 20 minutes.
Mash potatoes to desired consistency with a potato masher. Stir Colby-Monterey Jack cheese and cream into potato mixture, return soup to a simmer, and cook until cheese melts and soup is hot, about 15 minutes more. Season with salt and pepper. Remove and discard bay leaves.
Ladle soup into bowls and top with chives.
For a smoother soup, blend on low speed with an electric mixer instead of the potato masher. It may be necessary to add more chicken broth because this will make the soup thicker. Add chicken broth so that the soup is the desired consistency.
There is no salt on the ingredients list because the cheese itself is quite salty.
You can substitute chicken broth for the chicken stock. You can substitute vegetable bouillon for the chicken bouillon. You can substitute half-and-half for the heavy whipping cream.
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