Mini Mushroom Galettes

Dough

• 10 ½ oz all-purpose flour
• 3 oz water, ice cold
• 6 oz unsalted butter, diced
• 2 - 3 pinches ground nutmeg (optional)
• 1 tsp salt

Filling

• 3 oz Gruyère cheese, cut into pieces
• 1 oz Parmesan cheese
• 4 oz yellow onion, cut into pieces
  or 4 oz shallots, cut into pieces
• 1 oz unsalted butter, cut into pieces
• 2 sprigs fresh thyme, leaves only, plus extra to garnish
• 2 garlic cloves
• 14 oz fresh mixed mushrooms (e.g. , cremini, button, king trumpet, chanterelles, boletes, oyster mushrooms), sliced
• ½ tsp salt
• ⅛ tsp ground black pepper
• 2 oz mascarpone cheese
  or 2 oz crème fraîche
• 1 large egg, whisked, to brush