Melt butter and olive oil in a large pot over medium-high heat; add leeks, onion, garlic, bay leaves, and coriander and sauté until onions are 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.