In a saucepan over medium heat, saute carrot, celery, onion, garlic and ham in canola oil until lightly brown, about 10 minutes. Rinse clams under running water, drain. Add clams and clam juice, continue to cook slowly to reduce volume by half. Add milk, stock, seasonings, potatoes and rice.
Bring to simmer, reduce heat and cook for 1 hour, until rice is cooked and stew has thickened considerably. Serve.