Heat the olive oil in a small skillet over medium heat. Add the chopped onions and sauté for 4-5 minutes, until tender. Add minced garlic and continue cooking 1 minute, stirring frequently. Remove from heat and transfer mixture to a container to cool off.
While the onion is cooking, you can chop the artichokes, olives, capers, and parsley.
Mix all the chopped ingredients together with the red onion mixture, tossing with a fork to blend. Add the mayonnaise and again stir to blend.
Add the Parmesan cheese and stir until combined with artichoke mixture. It may seem stiff. That’s ok.
Preheat broiler in oven.
Spread a couple of teaspoons of artichoke mixture on each slice of bread, trying to make it even. Place on baking sheet (I covered mine with foil.), leaving a bit of space between each piece of bread. Broil for 2-5 minutes or until edges of bread are golden brown and artichoke mixture is bubbling and bronzed.
Transfer to serving platter and make your guests happy!