For the ham steaks: Heat the oil on a cast-iron griddle over medium-high heat. Add the ham steaks and cook until golden brown on both sides, about 4 minutes per side.
For the apple-mustard chutney: Melt the butter in a medium saucepan over medium-high heat. Add the apple and onion and cook until softened, about 3 minutes. Add the apple cider vinegar, brown sugar, mustard seeds and some salt and pepper. Cook until thickened, about 5 minutes. Serve the chutney over the ham steaks.