Rainbow Potato Stacks

Name: Rainbow Potato Stacks
Ingredients: 3 medium russet potatoes, preferably narrow (1 to 1 1/2 pounds total); 2 medium regular or purple sweet potatoes, preferably 1 of each (1 to 1 1/2 pounds total); 4 ounces Gruyère cheese, shredded (about 1 cup); 1 3/4 ounces Parmesan cheese, finely grated (3/4 cup); 2 cloves garlic; 4 large sprigs fresh sage; 7 to 8 sprigs fresh thyme; 8 tablespoons (1 stick) unsalted butter; 2 1/2 teaspoons kosher salt; 1/2 teaspoon freshly ground black pepper; Flaky salt, for garnish