In a mixing bowl, whisk together the gluten-free flour, eggs, milk, and a pinch of salt until you achieve a smooth batter. Allow the mixture to rest for 30 minutes at room temperature.

Heat a non-stick skillet over medium heat and lightly grease it with butter. Pour a small amount of batter into the skillet, swirling to create thin layers. Cook for 1-2 minutes until the edges begin to lift and the bottom is golden brown, then flip and cook for another 1-2 minutes. Keep the crepes warm under a clean towel as you repeat the process.

In a large skillet, melt a tablespoon of butter over medium heat. Add sliced leeks and diced mushrooms, sautéing until they are golden and fragrant, which should take about 5-7 minutes. Once tender, stir in shredded chicken until heated through.

In a separate saucepan, melt 2 tablespoons of butter over medium heat. Whisk in an equal amount of gluten-free flour, cooking for about 1 minute until bubbly. Gradually pour in milk, stirring continuously for 5-7 minutes until the sauce thickens to a creamy consistency. Season with salt and pepper to taste.

Preheat your oven to 350°F (175°C). Lay out each crepe and spoon a generous amount of the chicken filling down the center. Roll them up and place in a greased baking dish. Pour the béchamel sauce over the crepes and sprinkle with grated Gruyere cheese. Bake for 20-25 minutes, or until bubbly and golden brown.