In a medium skillet, heat olive oil over medium low heat. Shave or thinly slice asparagus and dice green onion. Toss green onion and garlic in with olive oil and heat for 2-3 minutes, just until fragrant. Add in asparagus and heat until asparagus turns a nice bright green color, only another 2-3 minutes. Sprinkle with salt and pepper, set aside.
Whisk together flour, salt, eggs, milk, and melted butter until smooth. Heat 8″ skillet and lightly grease with oil. Place a scant 1/4 cup of batter in pan. Tilt the pan so that the batter covers the entire pan and cook for about 30 seconds. Flip and cook for another 15 seconds. Place done crepes on a piece of parchment paper (be sure not to fully stack crepes.)
Once crepes are finished (this will make about eight) place a couple spoonfuls of asparagus and a bit of mozzarella on half the crepe. Fold over to cover the filling, then fold again to form a 1/4 circle.
Return crepe to pan over medium low heat and cook until each side is golden brown and mozzarella has melted. Serve with a slight drizzle of olive oil and extra green onions.