01 - Whisk together flour, eggs, milk, melted butter, and salt in a bowl until smooth. Cover and let rest for 15 minutes.
02 - Heat a nonstick skillet over medium heat and lightly grease with butter or oil. Pour 1/4 cup batter into the pan, swirl to coat the bottom. Cook for 1 to 2 minutes until edges lift, flip and cook another 30 seconds. Repeat to make 8 crêpes. Stack and keep covered.
03 - Melt butter in a large skillet over medium heat. Add onions and cook until translucent, about 2 to 3 minutes. Add mushrooms and sauté until softened, 4 to 5 minutes. Stir in flour and cook for 1 minute.
04 - Gradually whisk in milk and chicken broth. Cook, stirring frequently, until the sauce thickens, about 3 to 4 minutes. Stir in chicken, thyme, salt, pepper, and parsley. Heat through and adjust seasoning to taste.
05 - Place a crêpe on a plate and spoon 2 to 3 tablespoons of filling along the center. Roll or fold the crêpe around the filling. Repeat with remaining crêpes and filling.
06 - Arrange filled crêpes in a baking dish, sprinkle with grated cheese, and broil for 2 to 3 minutes until cheese is melted and golden.
07 - Serve warm, garnished with extra parsley if desired.