heat gas grill to high or prepare a hot charcoal fire. Pry open the apricots and put a piece of cheese and almond into each one. Wrap a piece of bacon around each apricot, trimming as needed so it overlaps by 1/2 inch, and secure it with a wooden pick. Season the apricots all over with pepper.
Reduce the grill heat to medium, or scatter the coals a bit or raise the grate if using charcoal. Use tongs to grill the apricots on all sides with the grill open, propping them between the bars to hold up on the narrow side. move the apricots around often to avoid flareups. Cook until the bacon is crisp all over, about six minutes total. Serve at once