Rub the insert of a 6-quart slow cooker very lightly with the butter on the bottom and 2 inches up the sides.
Whisk together the cream, broth, flour and thyme in a 2-cup measuring cup.
Arrange 1/3 of the sliced potatoes in an even and slightly overlapping layer on the bottom of the slow cooker insert. Sprinkle 1/3 of the Gruyere over the potatoes, and add 3/4 teaspoon salt and an even grating of black pepper. Drizzle 1/3 of the cream mixture evenly over the layer. Repeat with 2 more layers of potatoes, Gruyere, salt, pepper and cream mixture.
Press the potatoes down firmly to make sure they are submerged. Cover the slow cooker, and cook on high until the potatoes are tender and the liquid has thickened, 4 1/2 to 5 hours. Remove the lid, and let the potatoes rest for 15 minutes. (The sauce may seem thin at first, but it will thicken as it sits.)
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