Heat an extra-large skillet over medium heat. Add walnuts; cook and stir about 2 minutes or until toasted. Remove nuts from skillet and set aside.
To assemble sandwiches, spread one side of each of four of the bread slices with bruschetta topper; spread one side of the other four slices with mayonnaise. Layer nuts, turkey, and spinach on top of the bruschetta-spread slices. Top with other slices, mayonnaise sides down. Brush the outsides of the sandwiches lightly with oil.
Place the sandwiches in the heated skillet. Place a large skillet on top of sandwiches, weighing down by adding a few cans of food to top skillet. Cook for 2 minutes; remove top skillet. Turn sandwiches; replace skillet and cans. Cook about 2 minutes more or until golden and heated through.