Preheat the oven to 400 degrees F (200 degrees C). Line a large baking sheet with parchment paper.
Heat 2 teaspoons oil in a skillet over medium heat. Add onions; cook and stir until translucent, 6 to 8 minutes. Sprinkle in chili powder and mix. Add turmeric, 1/2 teaspoon coriander, 1/4 teaspoon cumin, and 1/4 teaspoon ginger. Stir well and remove from heat.
Combine chickpea flour, 1/2 teaspoon cumin, 1/2 teaspoon coriander, and salt in a bowl and mix well. Mix in the onions and tomato puree; add a little water until mixture is wet and easy to stir.
Drizzle 1 teaspoon olive oil onto the prepared baking sheet. Place 2 tablespoons of the onion mixture onto the baking sheet for each bhaji; flatten slightly with the back of a spoon.
Bake in the preheated oven for 20 to 25 minutes. Drizzle remaining oil over the bhajis and continue baking until golden brown, about 25 minutes.
