Drain the artichokes and olives. Cut 10 slices from 4 olives. Cut grissini sticks into 10 equal pieces. Finely chop the artichoke hearts and remaining olives, season with a little pepper and mix.
Place the slices of ham next to each other on the work surface and spread the chopped ingredients on top. Place one grissini stick on each side of a slice of ham, roll it up loosely and place it on the table.
Put an olive slice on each grissini stick and arrange on plates.