Chop 1 1/2 apples into 1/2-in. dice. Coarsely chop remaining 2 1/2 apples, put in a food processor with all remaining ingredients except sliced almonds, and pulse until blended but still quite coarse.
Turn mixture into a bowl and stir in diced apples. Sprinkle with sliced almonds just before serving.
Make ahead: Up to 1 day (except toasted almonds), chilled.