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