Combine potatoes, spinach, onion, ginger, curry powder, and salt in a large bowl.
Heat oil in a large skillet over medium-high heat. Add the potato mixture and press into a layer. Cook, without stirring, until crispy and golden brown on the bottom, 3 to 5 minutes.
Reduce heat to medium-low. Fold in chickpeas and zucchini, breaking up chunks of potato, until just combined. Press back into an even layer.
Carve out 4 “wells” in the mixture. Break eggs, one at a time, into a cup and slip one into each indentation. Cover and continue cooking until the eggs are set, 4 to 5 minutes for soft-set yolks.