In a medium pot, heat the oil and butter over medium-high heat. Add the onion, leek, carrots, celery and potatoes and sprinkle with salt and pepper. Cook for 5 minutes or so, until the veggies are beginning to brown. Add the stock and bring to a simmer.
Reduce the heat and simmer for 20 minutes, or until the veggies are tender. With a hand-held immersion blender, purée about half of the soup, right in the pot, until smooth. (Alternatively scoop some out and puree it in the blender, then return it to the pot.)
Stir in the cream and heat through, then stir in the cheddar and remove the pot from the heat. Stir until the cheese melts, then serve hot.