Preheat the oven to 375°F. Slice ½ inch off the tops of the garlic heads to expose the cloves. Place on a large piece of tin foil. Drizzle with olive oil and season with salt.

Wrap the foil around the garlic and place on a baking sheet. Bake for 45-50 minutes or until the cloves are caramelized. Allow to cool slightly, then squeeze the cloves into a medium pot, reserving a few cloves for later.

Mash the remaining roasted garlic into a paste, then place the pot over medium heat. Add the half-and-half and thyme, stirring well. Season with salt and pepper.

Bring to a simmer, then reduce heat to low. Simmer for about 20 minutes.

Slice the potatoes very thinly using a mandoline or sharp knife. Arrange about a third of the potatoes in a buttered 9 x 13-inch baking dish. Top with a handful of shredded cheeses and drizzle some garlic cream over top.

Repeat this process two more times until all ingredients are used, ending with an extra handful of cheese on top. Scatter reserved roasted garlic cloves over the top.

Gently press everything down to ensure potatoes are submerged in the garlic cream.

Place the baking dish on a baking sheet and bake for 1½-2 hours, or until a knife easily inserts through the potatoes in the center. Allow to cool for at least 20 minutes before serving.