Combine dates, almonds, anchovies, shallots, black olives and vinegar in food processor. With motor running, slowly add enough grapeseed oil to make a paste. Scrape into a bowl and stir in orange zest.
Lay 6 slices of bread on wax paper. Spread each slice with divided olive paste and top one slice with cheese. Cover with other slice of bread, olive paste down, pressing gently.
Combine egg, milk and salt in pie plate. Dip each sandwich into mixture, one at a time, coating well. Using nonstick panini press, cook on medium high until golden. Repeat with remaining sandwiches. Slice diagonally if desired. Serve hot or warm.