Make the crepe batter by whisking together the flour, eggs, milk, melted butter, and salt until smooth. Let it rest for 15 minutes.
Heat a lightly greased skillet over medium heat and cook thin crepes, about 1/4 cup batter at a time, until set and lightly golden. Stack and keep warm.
Cook the asparagus in olive oil over medium heat for 3 to 4 minutes until crisp-tender. Remove and set aside.
In the same pan, melt the butter and sauté the shallot until soft, then add the garlic and cook for 30 seconds.
Stir in the flour and cook for 1 minute. Slowly whisk in the chicken broth and cream, then simmer until thickened.
Add the Parmesan, salt, and pepper. Stir in the chicken and asparagus and cook just until heated through.
Spoon the filling into each crepe, fold or roll, and serve warm.