In a large sauté pan, cook prosciutto slices over medium-high heat until crisp. Remove prosciutto, placing on plate; set aside.
Add butter or oil to sauté pan; when hot, add shallots and Brussels sprouts. Cook 8 to 10 minutes, stirring infrequently to allow cut sides to brown. After Brussels sprouts are browned, stir in white wine to deglaze pan. Sprinkle salt over top and stir to incorporate.
Place sprouts and shallots in serving dish, sprinkling crisped prosciutto and blue cheese over top immediately so cheese melts slightly. Serve promptly.