Hasselback Potato Gratin

Name: Hasselback Potato Gratin
Ingredients: 1/2 to 1 cup Gruyère cheese grated; 1/2 to 1 cup Parmesan cheese grated (plus more for garnish, if desired); 1 to 1 1/2 cups heavy cream; 2 to 3 medium garlic cloves minced; 1 heaping tablespoon fresh thyme leaves roughly chopped (more for garnish, if desired); Kosher salt and black pepper; 4 1/2 to 5 pounds Russet or Yukon Gold potatoes sliced 1/8-inch thick using a mandolin slicer; 1/2 large yam peeled and sliced 1/8-inch thick using a mandolin slicer