In a small bowl, mix the pestos together thoroughly with a fork until combined. Spoon 1 tablespoon of the pesto mixture on 1 side of both pieces of the bread and spread evenly with a butter knife.
Preheat a griddle or nonstick pan over medium heat.
Place the slices of prosciutto flat on the griddle to heat through and until slightly brown at the edges.
Place 2 slices mozzarella on 1 of the slices of pesto bread. Top with the tomato slices, the cooked prosciutto and the remaining 2 slices mozzarella. Finish by topping with the other slice of bread, pesto side down.
Spray the sandwich on 1 side with the olive oil spray. With a spatula, place the sandwich, sprayed side down, on the griddle. When sandwich is on the griddle, spray the other side.
When the cheese begins to melt on 1 side, use the spatula to flip the sandwich. Cook about 5 minutes on the other side.