Preheat oven to 375F. Place rack on lowest level in oven.
Butter two 8-oz. ramekins, and dust sides and bottoms with 1 Tbs. Parmesan each. Place on baking sheet.
To make Béchamel: Warm milk in saucepan. Melt butter in second saucepan over medium-low heat. Stir in flour until smooth, and cook 2 to 3 minutes, stirring with wooden spoon; allow to bubble but not brown.
Take pan off heat, whisk in warm milk and return to heat; whisk vigorously, scraping bottom and sides to prevent scorching. When mixture simmers, reduce heat to low, and cook, stirring often from sides and bottom, 5 minutes, or until thick. Season with salt, pepper and nutmeg. Remove from heat; stir 1 minute more. Beat in egg yolks 1 at a time.
To make Soufflé: Using electric beaters, beat 4 egg whites in bowl, starting at low and slowly increasing speed until they begin to foam. Add cream of tartar and salt, and beat until satiny peaks form and hold their shape; do not overbeat.
Combine remaining cheeses. Using rubber spatula, stir one-fourth of beaten whites into Béchamel. Pour Béchamel into center of remaining whites, and fold together. With each fold, sprinkle in handful of cheese mixture and handful of asparagus, giving bowl a quarter turn. When everything is added and mixture is uniform, carefully spoon into soufflé dishes. Put baking sheet on bottom rack.
Bake 20 to 25 minutes, or until puffy and browned; do not overcook—centers should be slightly runny. Serve.