Wild Mushroom Bread Pudding

Name: Wild Mushroom Bread Pudding
Ingredients: Unsalted butter, for greasing; 12 oz. thick-cut bacon, cut into 1/4″ slices; 1 1⁄2 lb. mixed mushrooms, such as cremini, oyster, and porcini, sliced 1/4″ thick; 2 1⁄2 cups whole milk; 1 1⁄2 cups heavy cream; 1⁄2 cup grated parmesan; 1⁄3 cup roughly chopped parsley; 2 tsp. minced thyme; 6 eggs; Kosher salt and freshly ground black pepper, to taste; 1 (1-lb.) loaf country bread, torn into 1″ pieces (6 cups), lightly toasted; 1 cup shredded Gruyère; 1 large leek, cut into 1/2-inch pieces