01 - In a bowl, whisk together flour and salt. Add eggs and half the milk, whisk until smooth. Gradually whisk in the remaining milk and melted butter. Let the batter rest for 15 minutes.
02 - Heat an 8–10 inch nonstick skillet over medium heat and lightly butter it. Pour in 1/4 cup batter, swirl to coat evenly, and cook until edges lift and bottom is golden, about 1 minute. Flip and cook an additional 30 seconds. Repeat to make 8 crêpes, stacking them with parchment paper in between.
03 - Melt 2 tablespoons butter in a large skillet over medium heat. Add diced onions and cook until softened, about 3 minutes. Add mushrooms and sauté until golden, about 5 minutes. Stir in garlic and cook for 1 more minute.
04 - Add shredded chicken, heavy cream, Gruyère cheese, and parsley to the skillet. Stir until cheese is melted and mixture is creamy. Season with salt and freshly ground black pepper. Remove from heat.
05 - Preheat oven to 375°F. Place one crêpe on a work surface, spoon 2–3 tablespoons of filling along the center, and roll up. Place seam-side down in a lightly greased baking dish. Repeat with remaining crêpes and filling.
06 - Sprinkle the assembled crêpes with remaining Gruyère cheese. Bake for 15–20 minutes until cheese is melted and bubbly. Serve hot, garnished with extra parsley if desired.