Make the crepes: Whisk the eggs together in a medium-size mixing bowl. Slowly add the melted butter and whisk until combined. Sift in the flour and salt and stir until combined. Slowly add in the milk. The batter should be runny. Strain the batter and let it rest, refrigerated, for at least 1 hour.
When you are ready to cook, put a little melted butter into a nonstick pan and put it over medium heat. Ladle the crepe batter into the pan tilting the pan while adding the batter to completely and evenly coat the bottom of the pan. This will take a little practice; usually the first crepe gets scrapped. Once the edge of the crepe begins to pull away from the pan, after about 1 to 2 minutes, use a spatula to get under the crepe and use your fingers to turn it over. The crepe should be golden brown. Cook for 1 minute on the other side, remove it from the pan, and put it onto a plate. Repeat making and stacking crepes, adding more butter to the pan as needed, until all the batter has been used.
Make the bechamel: In a medium saucepan over medium-high heat, melt the butter. Stir in the flour and cook for 3 to 4 minutes to cook out the raw flour flavor, but do not let it brown. Pour in the milk, whisking constantly to avoid lumps. Season with salt, lower the heat to medium, and cook until the sauce thickens, about 5 minutes. Remove the pan from the heat and stir in the cheese. Keep warm.
For the filling: Bring a large pot of salted water to a boil over medium heat. Add the asparagus and blanch for about 1 minute, just enough time to set the color but not to overcook it. Immediately plunge the asparagus into a bowl of salted ice water to stop the cooking. When the asparagus is cool, drain and cut it into 1-inch pieces, keeping the tips aside.
Heat a medium skillet over medium-high heat. Add the butter and shallots and cook until the shallots are soft, about 5 minutes. Pour in the wine and let it reduce by half. Add the chicken, tomatoes and chopped basil and cook until they are warmed through, about 3 minutes. Add the asparagus and 1 cup of the reserved bechamel. Taste and adjust the seasoning.
Lay a crepe on your work surface. Spoon a couple of tablespoons of the chicken mixture down the center of the crepe. Roll up the crepe like a cigar. Repeat with remaining crepes and filling. (Alternately, spoon the filling mixture over 1 half of the crepe, fold the crepe in half, then in half again to form a triangle).
To serve, put 2 crepes onto each serving plate. Spoon some of the bechamel sauce over the crepes and garnish with the reserved asparagus tips and some basil leaves. Serve immediately.