Preheat oven to 325 degrees F (165 degrees C). Grease a 10x7x2-inch baking dish.

Drain marinade from one jar of artichoke hearts into a skillet. Pour artichoke hearts from drained jar and the entire second jar (marinade and artichoke hearts) into a food processor. Blend until artichoke hearts are coarsely chopped and set aside.

Cook and stir onion and garlic in the skillet with marinade over medium-low heat until onions are light brown, 5 to 7 minutes. Remove from heat and transfer to a large bowl.

Stir onion mixture, eggs, bread crumbs, salt, black pepper, oregano, and hot pepper sauce together until well mixed.

Stir sharp Cheddar cheese, parsley, Parmesan cheese, and chopped artichoke heart mixture into the onion mixture. Pour mixture into prepared baking dish.

Bake in preheated oven until top is golden, 25 to 30 minutes. Cut into 1-inch squares and serve warm or cold.