In a medium bowl, combine the flour, sugar, and salt. In a big bowl, whisk the eggs and milk until well mixed. Beat in the flour mixture until smooth. An old-school whisk will do the job just fine. But if you have an immersive blender, it will make the batter even smoother. Then stir in 3 tablespoons of the melted butter. Cover with a plastic wrap and leave rest at room temperature for 30 minutes.
Heat 1 tablespoon of oil in a large sauté pan. Add the chicken and sauté until cooked all the way through and no longer pink, about 3-5 minutes. Make sure to bread large chunks with a spatula as the chicken cooks. Transfer the chicken to a bowl and set aside.
Heat 1 tablespoon of oil in the same skillet. Add the onion and cook until the onion is opaque for about 5 minutes. Add the sliced mushrooms and cook, covered with the lid. Stir the mixture frequently, and cook for about 10 minutes until the mushrooms are cooked all the way through.
Add the chicken to the mushrooms and season with salt and pepper to taste; mix well. Stir in the sour cream and adjust the seasoning. Transfer the chicken-mushroom filling into a medium bowl and let cool.
Meanwhile, make the crepes. Gently stir the batter with a whisk if it separates. Heat a 10-inch non-stick or crepe pan over medium-high heat until really hot. Cover the pan with a thin layer of oil, and pour a small amount of batter. Rotate the pan to spread the batter as thinly as possible. Cook over moderate heat until lightly browned on the edges, about 1 minute. Loosen the edges with a spatula and flip over the crepe. Cook on the other side for about 20 seconds. Transfer the crepe to a platter. Repeat with the remaining batter.
To assemble the crepes, place about two tablespoons of filling on the center of the crape, and then shape it as a beggar’s purse. Secure the top with a piece of a long green onion. Just wrap it around and tie it into a loose knot.