Rub the bottom of a 9x13 inch baking dish with olive oil. Combine the onion, carrot, spinach, rosemary, chickpea flour, water, salt, and olive oil in a medium saucepan and whisk until no lumps remain.

Place the pot over medium heat and and continue to whisk until mixture starts to become thick. Swap out the whisk for a rubber spatula and continue stirring until the mixture is very thick, about 8-10 minutes.

Pour the mixture into the prepared baking dish, then spread it out into an even thickness. Work quickly, as the mixture will start to seize up and become hard to spread. Transfer the baking dish to the refrigerator until the mixture is totally cooled and solidified, about 2 hours.

Remove from refrigerator, invert it on to a cutting board and slice into whatever shape you'd like.

Heat abut ½-1 inch of olive oil in a large saute pan over medium high heat (cast iron works best). Place several pieces in the pan, but be careful not to overcrowd it. Fry until golden brown, then flip and cook until browned on the other side. Remove the panelle and place them on paper towels to drain, then immediately sprinkle with salt while they're still hot. Repeat with the remaining panelle and serve immediately.