Melt about 3 tablespoons of butter in a medium-size skillet over medium heat. When it foams, add sage leaves and cook leaves to crisp and the butter is brown. Remove the leaves to a plate and reserve. Add onions to brown butter and cook 20-25 minutes to light caramel in color. Raise heat a bit, add apples and cook to tender-crisp, 5 minutes. Season with salt, pepper and nutmeg to taste.
 
Meanwhile, heat a large, cast-iron or heavy skillet over medium-high heat. When onions are half-cooked, season the chops with salt and pepper on both sides and add olive oil to the pan, 1 turn of the pan. Brown chops on both sides and edges then remove to a plate and reduce heat to medium. Add remaining tablespoon of butter to pan and when it foams, add shallots and garlic. Stir a minute or so; add stock and scrape up drippings. Add Worcestershire, soy sauce and maple syrup, and bring to bubble. Slide pork back in and turn in sauce to coat. Let sauce simmer 4-5 minutes to coat chops.