"Delicious, tender octopus stewed in white wine, butter, caramelized onions, ginger, and garlic. This is a re-creation from a dish I had in Puerto Viejo, Costa Rica at a restaurant called Koki Beach. It was pretty spot-on. It is advised to wear gloves when handling an octopus because some people get a skin reaction. Since I didn't have any available, and don't have any known food allergies, I took my chances and ended up ok and rash-free."
Heat 1 tablespoon butter and oil in a skillet over medium heat; stir in onion. Cook and stir until onion has softened and turned translucent, about 5 minutes. Reduce heat to low. Continue cooking, stirring frequently, until onion is very tender and dark brown, about 30 minutes more.
Rinse octopus. Place on a flat work surface and cut tentacles into thirds. Chop the head into bite-sized pieces. Place octopus pieces in a gallon-sized resealable plastic bag. Mix in salt and add crushed ice. Seal the bag and place into a larger grocery bag. Pound the octopus with the smooth side of a meat mallet until as tender as possible. Remove octopus from the bag and let drain in a colander.
Stir ginger and garlic into the skillet with the onion; cook until fragrant, 1 to 2 minutes. Pour in wine and the remaining 3 tablespoons butter. Increase heat and bring to a boil. Add octopus; reduce heat to a simmer. Cover and cook, stirring every 10 minutes, until flavors meld, about 1 hour. Uncover and continue simmering until sauce is thickened to your liking and octopus is tender, about 1 hour more.