Wrap the bricks in foil and set aside (these are your weights!)
Brush the outside of each focaccia slice with olive oil. Lightly brush the inside of one half of the focaccia with olive oil. Spread a thin layer of the sun-dried tomato pesto over the other half.
On the bottom half of each sandwich, place 1 slice of cheese, 2 slices of prosciutto, and then 1 more slice of cheese. Top with the remaining focaccia slices. Place the panini on a baking sheet to take out to the grill.
Prepare enough coals for a medium-hot charcoal fire, or preheat your gas grill on medium-high for 10 minutes with the lid closed.
When the coals are ready or the gas grill is hot, place the panini on the grill and weigh them down with the bricks. 1 brick should work for 2 panini. Grill for 3 minutes, making sure the bottom doesn't burn. Turn, place the bricks back on the panini, and grill for 3 minutes more. The cheese does not have to be completely melted; it'll still taste spectacular.
Slice each sandwich in half; serve immediately.