1. Bring 1 cup water to a boil in a large skillet. Add clams, cover, and steam 5 to 7 minutes or until shells open; discard any that do not. Drain clams, reserving cooking liquid. Pour cooking liquid through a fine wire-mesh sieve into a bowl, and set aside.
2. Cook bacon in a large saucepan over medium-high heat until crisp; drain on paper towels, reserving 2 teaspoons drippings in saucepan.
3. Sauté carrots, onion, and celery in hot drippings over medium-high heat 5 minutes or until tender. Add reserved clam cooking liquid, clam juice, and next 5 ingredients; bring to a boil. Reduce heat and simmer, uncovered, over medium heat 8 minutes or until potatoes are tender.
4. Meanwhile, shuck clams and coarsely chop the meat. Whisk together milk and flour in a small bowl; add to saucepan, and bring to a simmer, stirring occasionally. (Do not boil.) Add bacon and clams, and cook 1 to 2 minutes or just until heated through. Stir in parsley.