Bring a small pot of water to a boil. Add the asparagus and cook 1 minute. Drain asparagus, cool in cold water, and then drain well again. Carefully cut each asparagus tip in half lengthwise. Set on a plate and refrigerate until needed.
Line a baking sheet with parchment paper. Place the cream cheese in a medium bowl and beat until lightened. Mix in the sour cream, lime juice, curry powder and garlic and beat until smooth. Stir in the crab and green onion. Divide and spread the mixture on the baguette slices and place on the baking sheet. Top each melt with 2 half slices of asparagus. Sprinkle melts with Parmesan cheese. (Melts can be made to this point a few hours in advance. Cover and refrigerate until needed.)
Preheat the oven to 375 degrees F. Bake melts 10 to 12 minutes, until piping hot and light golden. Arrange on a platter and enjoy.
Note: After trimming off the tips for this recipe, reserve the remaining part of the asparagus spears for another recipe, such as a stir-fry or soup. The baguette used for this recipe was about 2 1/2" wide.