Peel, core, and chop the apples. Transfer 2 cups chopped apples to a small saucepan (reserve the rest). Add the apple cider, juice, or water, brown sugar, and cinnamon. Bring to a boil, then reduce the heat and simmer until the apples are very tender, 15 to 20 minutes. Coarsely mash or puree with an immersion blender. Set aside to cool slightly.

In a food processor, combine 2/3 of the apple mixture, chickpeas, almond butter, garlic, salt, cumin, and lemon juice. Process until blended, scraping down the sides as necessary. With the motor running, slowly drizzle in the olive oil. Check the consistency and blend in up to 1/4 cup water until the hummus is thick and creamy.

Transfer the hummus to a bowl. Finely dice the remaining apples and stir them into the hummus along with the remaining apple puree.