Tarte aux Champignons (Mushroom Tart)

Ingredients

• 1 1/4 cups all-purpose flour
• 1/2 teaspoon salt
• 1/2 cup (113g) cold unsalted butter, cubed
• 3-4 tablespoons ice water
• 2 tablespoons olive oil
• 1 lb (450g) mixed mushrooms (such as cremini, shiitake, and button), sliced
• 2 garlic cloves, minced
• 1 shallot, minced
• 1 teaspoon fresh thyme leaves
• Salt
• pepper
• 1/2 cup crème fraîche or heavy cream
• 2 eggs
• 1/2 cup grated Gruyère or Parmesan cheese
• Fresh parsley, chopped, for garnish