Heat oil in a medium pot over medium heat. Once hot, add the shallot, garlic, and ginger and cook until soft and fragrant, about 3-4 minutes.
Add the garam masala, salt, and turmeric, and cook for an additional 1 minute, then add the apple cider vinegar and raisins and cook for 1 minute more.
Add the apples and brown sugar, stirring to mix well. Heat until liquid in the bottom of the pot starts to boil, then reduce heat to low and cover (it will seem like there is hardly any liquid, but resist the temptation to add more here as the apples will release a lot of liquid as they cook down).
Continue to cook, covered, over low heat for about 20 minutes, giving the chutney a good stir every 5 minutes or so.
Remove cover from pot and use a fork or potato masher to mash cooked apples to a chunky consistency. Continue to cook, uncovered, until most of the liquid has evaporated, about 8-10 minutes. Eat immediately, or refrigerate in an airtight container for up to 1 week.