Brush all sides of each focaccia half with olive oil. On the bottom portion of each sandwich, place a slice of ham, then the olives, then the red pepper strips, then the cheese, then the other slice of ham. Top with the remaining focaccia slices. Place the panini on a baking sheet to take out to the grill.
Prepare a medium-hot fire in your grill. Have a heavy cast-iron skillet, 2 foil-wrapped bricks, a cast-iron bacon press, or 2 heavy-duty grill spatulas by the grill.
Place each panini on the grill rack and weight or press down. Grill for 3 to 4 minutes on each side, or until you have good grill marks and the cheese has melted. If necessary to weight them down properly, grill these one at a time.
