Heat grill to high. Place a wire rack greased with olive oil on the grill while it heats up
Spoon out the pulp of the halved tomatoes. Add the pulp to a bowl with the olive oil, salt, and pepper for the grilled tomatoes.
Smash the ingredients together with a fork to combine. Set aside.
Sprinkle the seeded tomato halves with a little more salt and an extra drizzle of olive oil.
Add tomatoes, cut side down, to the wire rack and cook for about 15 minutes. Flip the tomato halves and spoon the pulp mixture over the them. Cook another 15 to 20 minutes. They should be shriveled and cooked through. Primarily you want to make sure that they've reduced in height by at least half.
Cut the loaf of bread into two 9-inch pieces. Slice each piece of bread in half laterally.
Spread the cut sides of the bread with the pesto, dividing evenly between the four pieces.
Layer the bottom halves with equal amounts of prosciutto and salumi. Top with mozzarella slices, then three tomato halves each. Finally top with the other halves of the bread.
Serve immediately or keep wrapped in aluminum foil in the refrigerator until ready to serve. You can totally make these sandwiches the day before! Just make sure you get a nice, crusty loaf of bread so it doesn't get soggy.