Whisk the chickpea flour, cornstarch, baking powder, cumin seeds, cayenne and 3/4 teaspoon salt in a bowl. Add 2/3 cup water and whisk until smooth. Add the onion, chickpeas, spinach and ginger to the batter and mix to combine.
Heat 2 inches of vegetable oil in a deep heavy-bottomed pot until a deep-fry thermometer registers 325 degrees. Working in batches, drop heaping tablespoonfuls of batter into the oil (do not crowd the pan). Cook until lightly golden, about 2 minutes, turning as needed. Transfer with a slotted spoon to a paper-towel-lined plate. Cool slightly, then gently press each fritter into a small disk, about 1/3 inch thick.
Return the fritters to the hot oil and fry until crisp and golden brown, about 1 more minute. Season with salt and serve with chutney.