Put the chickpeas and baking soda in a medium bowl and add cold water to cover. Let soak overnight. The next day, drain and rinse the chickpeas and transfer to a heavy pot. Add water to cover by 1 inch, bring to a boil over high heat, then lower the heat so the liquid is simmering. Simmer until tender, 1 to 2 hours, then drain, reserving the cooking liquid, and set aside.
Meanwhile, in a large frying pan, heat ½ cup of the olive oil over medium heat. Add the onions and half of the sage and cook, stirring often, until the onions are very soft and golden brown, 25 to 30 minutes.
Preheat the oven to 375°F. Put the cooked onions and sage leaves in a food processor and add half of the cooked chickpeas. Process until almost smooth, adding a bit of the bean-cooking liquid as necessary to aid the blending. Transfer to a large bowl and add the remaining (whole) cooked chickpeas. Mince the remaining sage leaves and stir into the batter with the red pepper flakes and salt.
Using your hands, squeeze the batter to crush the whole chickpeas slightly. Stir in the eggs and Parmigiano-Reggiano cheese. Grease a 9-inch ovenproof frying pan or cake pan with the remaining 2 tablespoons olive oil. Spoon the chickpea batter into the pan, smoothing the top, and bake until browned on top and set, about 1 hour. Let cool on a wire rack then cut into wedges and serve warm or at room temperature. Serve with a salad for a light lunch or dinner.