Heat canola oil in a large Dutch oven over medium-high heat until hot. Sear pork slices until well browned on both sides, then remove. Stir in the garlic and ginger, cook until fragrant, about 30 seconds. Add the water, soy sauce, brown sugar, and miso; bring to a simmer, scraping the bottom of the pan to dissolve the caramelized juices.
Place pork into pot, add additional water if needed to cover pork with the sauce. Then, reduce heat to medium-low, cover, and simmer for 3 hours until the pork is tender, and the sauce has thickened.