Potato gratin with mushrooms and blue cheese

Name: Potato gratin with mushrooms and blue cheese
Ingredients: 3 tablespoons unsalted butter; 3 leeks, washed and sliced (white parts and a little of the light green); 1 pound mushrooms, sliced; 1 1/2 t fresh thyme, chopped; 1 1/2 teaspoons fresh rosemary, chopped; Kosher salt and pepper to taste; 2 1/2 pounds yukon gold potatoes, cut in 1/8 slices; 4 ounces crumbled goat cheese; 4 ounces gorganzola or other creamy blue cheese; 4 tablespoons grated Parmigiano Reggiano cheese; 2 cups cream; 1/2 cup milk