In a pot, melt butter over medium heat. Add leeks, chopped onion, carrot and garlic. Saute and stir vegetables until they are glossy and have started to soften.Typically 5-10 minutes. Make sure carrots are cooked or you will have hard pieces in your soup
Stirring continuously, sprinkle in the flour. Keep stirring. Pour in chicken broth. Add the potatoes and bring to a boil. Reduce heat to maintain a simmer and cook covered until potatoes are soft enough to be easily pierced with a fork. (typically 15 minutes or so)
Put the cheddar cheese in a large heatproof bowl. Ladle some of the hot liquid from soup into cheese and stir with a wooden spoon until cheese melts and is blended. Carefully pour cheese into the potatoes and stir until mixed. Stirring, slowly pour in the cream and add salt and pepper. Continue to heat until it is almost back to boiling. Turn off, adjust seasonings and transfer to serving bowl. Garnish with chives or scallions and corned beef.