Blanch the asparagus spears in lightly salted boiling water for 2 minutes. Drain well and refresh under cold water. Pat dry.
Lay a slice of prosciutto flat on a board and top with 3 asparagus spears, a slice of pepper, a thyme sprig, an anchovy fillet and 3 more asparagus spears. Roll up into a parcel and secure with cooking string. Repeat to make 4 parcels.
Cook on a medium barbecue for 6—8 minutes, turning frequently, until evenly charred and tender. Serve the parcels with aïoli.