Gather the ingredients.

Make the crêpes: Combine flour and salt in a large bowl. Whisk milk, eggs, and melted butter together in a separate large bowl. Whisk egg mixture into flour mixture until smooth; cover and refrigerate for 1 hour. Strain the mixture into a clean bowl.

Heat a small nonstick skillet or crêpe pan over medium heat; brush the pan with butter. Pour 2 tablespoons of batter into the skillet and immediately rotate the skillet to spread batter out in a thin layer. Cook until the top of the crêpe is no longer wet and the bottom has turned light brown, 1 to 2 minutes.

Run a spatula around the edge of the skillet to loosen crêpe; flip crêpe and cook until the other side has turned light brown, about 1 minute more.

Preheat the oven to 350 degrees F (175 degrees C). Make the filling: Melt 3 tablespoons of butter in a skillet over medium-high heat; stir in garlic and thyme. Add chicken; cook and stir until heated through, about 5 minutes. Stir in cream cheese until melted and smooth.

Remove skillet from the heat; spoon chicken mixture evenly into the center of each crêpe and fold over. Place in a shallow casserole dish, overlapping slightly. Melt the remaining 2 tablespoons of butter and drizzle over crêpes.

Cook in the preheated oven until warmed through, about 10 minutes. Sprinkle with parsley before serving.