Heat oven to 325 degrees F.
Combine cream, salt, black pepper, garlic (peel the cloves and smash them gently with the palm of your hand) and thyme in a small saucepan. Place over medium heat and heat, stirring constantly, until the cream starts to bubble, 4 to 6 minutes. When cream starts to bubble, remove it from heat and continue stirring until it cools slightly. Let the cream sit while you prepare the rest of the dish (this will infuse the cream with flavor).
Heat a large (12 inch) oven-safe skillet over medium-high heat. Add butter. When butter melts, add shallots and kale leaves. Saute until kale is tender and bright green, ~4 minutes. Turn off the burner under the kale.
Use a food processor or mandolin to slice the potatoes into 1/8 inch slices. (I think the dish is more beautiful with the peels on, but you can peel the potatoes first if you prefer.)
Add the potatoes to the skillet, fanning them out over top of the kale.
Use a slotted spoon to remove the garlic and thyme from the heavy cream. Pour heavy cream over potatoes.
Cover the skillet tightly with foil and bake until the potatoes are tender, 75 to 85 minutes.
Remove skillet from the oven and turn on the oven's broiler. Discard foil.
Sprinkle both types off cheeses over the potatoes, tucking some of the cheese between the potato slices.
Return the skillet to the oven and broil until the top is golden brown, 5 to 6 minutes. (Keep a close eye on it to prevent burning.)