Combine mangoes, apple cider vinegar, sugar, brown sugar, onions, garlic, black pepper, salt, cayenne pepper, cinnamon, ginger, clove, allspice, mustard powder, raisins, carrots, and apples in a large bowl.

Cover the bowl and refrigerate overnight (approximately 12 hours).

Transfer the mixture to a large, heavy-bottomed saucepan.

Bring the mixture to a boil over medium-high heat.

Reduce the heat to low and simmer for about 30 minutes, or until the chutney reaches a syrupy consistency.

Let the chutney cool completely.

Refrigerate the chutney and use within a couple of days.

For longer storage, ladle the hot chutney into hot, clean pint or half-pint canning jars, leaving about 1/4-inch of headspace.

Seal the jars with new two-piece canning lids.

Process the sealed jars in a boiling water bath for 10 minutes.

Cool the jars completely.

Label the jars with the date and contents.

Store the jars in a cool, dark place.