Melt the butter in a small saucepan over low heat. Stir in the chopped garlic and set aside. Slice the baguette in half horizontally, then cut into sandwich-size pieces. Brush each piece with garlic butter.
Trim the ends of the asparagus. Coat with a thin layer of olive oil.
Heat the grill to medium hot. Grill the asparagus, rolling frequently, until just cooked and slight charred. Remove from heat and cut to sandwich-sized lengths. Grill the buttered baguette.
To assemble the sandwich, spread the cheese on the bottom half of the sandwich, layer the asparagus and top with the prosciutto.