In a large skillet, heat olive oil over medium heat; add garlic and red onion; cook for 10 minutes, or until onion is soft. DON'T LET GARLIC BROWN! Add remaining ingredients and simmer for 15 minutes, stirring occasionally. Set aside and keep warm.
While salsa is simmering, combine ingredients for fish including olive oil, lemon juice, parsley, and salt and pepper in a small bowl; beat with a fork to make sure the salt has dissolved. Pour over the fish and set aside.
Preheat outdoor or indoor grill or place fish on a broiler pan. Cook fish 4 to 5 inches from heat source for 4 to 5 minutes, depending on thickness; turn and cook for another 4 to 5 minutes, or until cooked through. Test with a fork: fish should pull away gently and be opaque in the middle. Top with Mediterranean Salsa and serve.