Add the potatoes, onion, celery, broth, thyme, pepper, salt, and the juice from the canned clams to the slow cooker. Set the clams themselves aside in the fridge.
Cover and cook on low for 5–6 hours, until the potatoes are fork-tender.
In a small bowl, stir the cornstarch into cold water until smooth.
Stir the cornstarch slurry, butter, and heavy cream into the slow cooker.
Add the reserved chopped clams. Cover and cook on low for 30 more minutes, until the chowder thickens and the clams are heated through.
Taste and adjust salt and pepper. Ladle into bowls and top with parsley or chives. Serve warm.