Preheat oven to 350°.
Lightly coat both sides of tomatoes with cooking spray. Arrange tomatoes in a single layer, cut sides up, on a jelly roll pan coated with cooking spray. Sprinkle evenly with oregano and salt. Bake at 350° for 1 hour.
Combine dill, pepper, and cheese; spread 1 tablespoon over each bread slice. Arrange 4 tomato halves and 1/4 cup arugula on each of 4 bread slices. Top with remaining bread slices. Serve immediately.