Over medium heat in a medium sized skillet add one tablespoon of olive oil and one tablespoon of butter and saute onion and garlic for three minutes or until onions are translucent.
Add blanched asparagus and salt and pepper to taste and cook for one minute.
Add the jar of artichoke hearts including the juice and 2 tablespoons of parsley. Let the mixture cook for about five minutes or until about half of the liquid has reduced. Then transfer out of pan into a separate bowl, cover and set aside.
Cook for three minutes and add one tablespoon of butter to the pan and flip the fish over.
Add the other half of lemon juice on the cooked side of the fish and finish cooking for roughly five to six minutes.
After fish is cooked turn flame on low and add tomato, capers and remaining parsley. Also add the heavy cream and stir. Add salt and pepper to taste.