1. Preheat your oven to 375°F (190°C).

2. In a large skillet cook the ground beef over medium-high heat breaking it up with a spoon until it's no longer pink. Remove from heat and set aside.

3. In a separate skillet melt 30 grams (2 tablespoons) of butter over medium heat. Add the sliced mushrooms and cook until tender for about 5 minutes. Add 15 grams (1 tablespoon) of all-purpose flour and cook for 1 minute stirring constantly. Gradually add 250 milliliters (1 cup) of beef broth and 120 milliliters (1/2 cup) of heavy cream whisking until smooth. Bring to a simmer and cook until the sauce has thickened for about 5 minutes. Season with salt and pepper to taste.

4. In a large bowl combine the sliced potatoes 60 grams (4 tablespoons) of melted butter salt and pepper. Toss until the potatoes are evenly coated.

5. In a greased 23x33-centimeter (9x13-inch) baking dish create a layer of potatoes. Top with a layer of the beef mixture then a layer of the mushroom sauce. Repeat this process until all the ingredients have been used finishing with a layer of potatoes on top.

6. Bake the gratin in the preheated oven for 45-50 minutes or until the top layer of potatoes is golden brown and the casserole is hot and bubbly. Remove from the oven and let rest for 10 minutes before serving. Garnish with chopped fresh thyme leaves if desired.