In a Dutch oven, cook bacon over medium heat until crisp. Remove bacon, drain on paper towels, and crumble. Reserve. Drain clams, reserve juice.
Cook and stir carrot, celery, and onion in bacon fat until onion is transparent.
Stir in flour, cornstarch, potatoes, salt, and pepper. Cook and stir until mixture is bubbly. Add reserved clam liquor to clam juice to measure 3 1/2 cups; stir juice and milk into the vegetable mixture. Heat just to boiling, and reduce heat to simmer. Cook, stirring occasionally, until mixture thickens.
Add clams, potatoes, and cheese; stir until cheese is melted. Sprinkle with reserved bacon, and garnish with chopped parsley.