1. Melt 2 tablespoons butter and 1 tablespoon oil in a saucepan over medium heat. Add onion, parsley, thyme, marjoram, bay leaf, and 1/2 teaspoon salt, and cook until the onions are brown but not burned. Stir occasionally.
2. Add the cider and cook until the liquid is reduced by half. Add flour and stock. Stir with a spoon to break up any lumps. Bring to a boil, turn down heat, and simmer for about 5 minutes while stirring occasionally. Set the sauce aside.
3. Melt 1 tablespoon butter and 1 tablespoon oil in a large skillet over medium heat. Add the mushrooms and 1/4 teaspoon salt, turn the heat to high, and cook for 3 minutes while stirring often. Remove from heat, turn the mushrooms into a bowl, and set aside.
4. Melt another 1 tablespoon butter and 1 tablespoon oil in the skillet over medium-high heat. Add boiling onions, garlic, carrots, and parsnips, and cook for 5 minutes, stirring occasionally. Add the mushrooms and half the sauce, cover pan, lower heat, and simmer for 5 minutes, stirring occasionally.
5. Add the remaining sauce. Raise the heat to medium and cook for 5 minutes, stirring occasionally. Add salt and pepper to taste.
6. Place potatoes in a saucepan and cover with about 2 inches (5 cm) of water. Add 1 teaspoon salt, and boil for about 15 minutes until tender. Drain off the water.
7. Put the potatoes back into the pot, with 1/3 cup butter (75 g), 2/3 cup cheese, and thyme, and mash until smooth. A few lumps are okay. Add salt and pepper to your taste.
8. Remove the bay leaf from the filling and turn into an 8-by-12-inch (20-by-30-cm) baking pan. Evenly spread the potato mixture over the filling. Sprinkle the remaining cheese over the top.
9. When ready to bake, preheat the oven to 375°F (190°C) and bake for 35 to 40 minutes.
Note: If you have any leftover Brussels sprouts from Thanksgiving dinner, pop them into the filling, too