Chop onion, tomato, and olives. Place in a medium bowl.
Add crumbled feta, mayonnaise, oregano, salt, and pepper. Blend well. NOTE: Make ahead to this point if desired, then refrigerate until ready to assemble and cook.
To assemble and cook:
Preheat broiler about 5 to 10 minutes before ready to cook.
Slice half of the baguette into 1/2-inch-thick pieces, cutting straight across for smaller rounds, or on the diagonal for larger, oblong shapes.
Place slices on an ungreased baking sheet. Spread a spoonful of the tomato mixture on each slice. Sprinkle some Parmesan on top. Cut more of the baguette as needed to use all of the tomato mixture.
Broil about 3 minutes, or until the cheese has melted and is lightly browned.
Garnish with fresh parsley, either by chopping and sprinkling some over the melts, or by placing sprigs around them. Serve immediately.