In a pan with a drizzle of olive oil over medium heat, add in the leeks, butter, garlic and mushrooms. Cook until the leeks and mushrooms are softened.
Add in the white wine to deglaze, then add the miso, mix well to dissolve the miso. Continue cooking until the white has evaporated. Season with salt and pepper. Transfer to a plate to cool completely in the fridge.
Pre-heat the oven to 180C/350F.
I patched a few sheets of puff pastry to create a bigger circle. Place 1/2 cup of gruyere cheese on the puff pastry circle, leaving a 4cm border. Top with the cooled mushroom mixture, spread the mixture evenly and maintain the border. Top with the remaining cheese. Carefully place the slices of potato in a spiral pattern on top of the mushroom and cheese layers.
Fold the puff pastry border over and brush with egg wash. Bake for ~1 hour or until the potatoes are soft, golden and the pastry is also golden brown. Let the galette slightly cool before serving