Potato and Turnip Gratin with an Herb Cream

Name: Potato and Turnip Gratin with an Herb Cream
Ingredients: Herb Cream; 1 tablespoon butter; 1 anchovy fillet; 1 tablespoon thyme leaves; 6 sage leaves; 2 tablespoons rosemary; 1 garlic clove, smashed; 1 1 inch thick slice onion; 3/4 cup cream; 1/4 cup whole milk; Gratin; 3 cups or approx 20 oz. sliced shitake mushrooms (or a mix of wild mushrooms); 3-4 turnips, peeled; 3-4 yukon gold potatoes, washed (I don't peel them but you can if you prefer); 1/2 cup gruyere, grated; 1/2 cup parmesan, grated.; salt and pepper