Wash and thoroughly pat dry the sweet potatoes. Using a fork, prick a few holes all around.
Preheat oven to 375F then bake for 55-70 minutes, depending on the size of the sweet potatoes. Alternatively, you can air fry the sweet potato at 400F for 35-45 minutes. To ensure they are cooked through, insert a toothpick or chopstick and it should pierce easily. Scoop flesh of sweet potatoes into a bowl and mash with a fork.
In a large skillet, melt butter then sauté onions until soft and fragrant. Add mashed sweet potatoes, salt, a few cracks of black pepper and mix until well combined, about 2 minutes. Remove from heat and let cool until warm to the touch.
Shape the croquettes by scooping about ¼ cup of the mixture and shape into flat, oval patties with your hands. This makes about 8-10 total patties. Place on a tray lined with parchment paper and refrigerate for 30 mins to firm up.
While the croquettes are in the fridge, make the katsu sauce by combining worcestershire sauce, ketchup, sugar, and oyster sauce and mix well. Set aside.
Setup your breading station but adding flour, beaten eggs, and panko breadcrumbs on separate plates. Dredge each patty lightly in flour, then dip in beaten egg, then coat with panko, pressing gently to ensure the breadcrumbs stick.
In a large skillet, add neutral oil until about 1 inch from the bottom. Heat oil to 350F and shallow fry the croquettes in batches (without overcrowding) until golden brown and crispy, about 2-3 minutes per side. Drain on a wire rack.