For this recipe, use 2 8-inch heavy frying pans.
Cut the mushrooms in large pieces. Heat 2 tablespoons of the fat or oil in a frying pan and add the mushrooms, salt and pepper. Sauté briskly, stirring, until mushrooms are tender, and all moisture has evaporated. Stir in garlic, shallots and parsley and taste for seasoning.
Preheat oven to 375 degrees.
Cut the potatoes in 1/8- inch slices, if possible using a mandolin slicer or a food processor.
Heat 2 tablespoons of the fat or oil in the frying pans for 1 minute. Remove and arrange potato slices overlapping in circles. Sprinkle them with salt and pepper and spread half of the mushrooms on top.
Cover mushrooms with another layer of potatoes, and spoon over some fat. Press a piece of foil with a weight on top.
Repeat with the other galette. Cook galette on top of the stove until underside starts to brown, 8-10 minutes.
Transfer to oven for 15-20 minutes or until potatoes are tender. Remove foil and weight and flip galettes in the pans. Continue cooking until underside is brown