Put vinegar into a small heavy-bottomed saucepan and simmer over medium heat until reduced by about two-thirds and slightly syrupy, 8-10 minutes. Remove pan from heat and set aside to let syrup cool.
Meanwhile, steam asparagus in a steamer basket set over a pot of boiling water over high heat until just tender, about 4 minutes. Set asparagus aside to let cool.
Lay 1 slice of prosciutto on a clean surface with one of the narrow ends closest to you. Put 2 asparagus spears on end closest to you, perpendicular to prosciutto, with tips facing in the same direction, then roll up prosciutto around asparagus and set aside. Repeat with remaining prosciutto and asparagus.
Working in 3 batches, melt 1 tbsp. butter in a large cast-iron or other heavy-bottomed skillet over medium-high heat. Add 6 of the asparagus-prosciutto bundles, judiciously season with salt, and cook until browned on each side, about 45 seconds per side. Transfer to a large warm plate. Repeat process twice with remaining butter and asparagus-prosciutto bundles.
Drizzle some of the vinegar syrup on each of the warm plates, then divide asparagus-prosciutto bundles evenly between plates.