Remove the stem of the eggplant and chop into 1-inch cubes. Place the cubes in a colander and toss them with the tablespoon of salt. Set aside for an hour in the sink.
After an hour, rinse the eggplant (to remove excess salt) and thoroughly pat the cubes dry with paper towel or clean kitchen towels.
Set up a dinner plate with a couple paper towels on top. In a wide, deep braiser-style pot or deep skillet, heat the oil over medium heat. In batches, sear the eggplant until it’s golden brown on all sides and softened. As the eggplant finishes, remove it from the pot with a slotted spoon and place it on the paper towel-lined plate. Set aside.
If necessary, add more oil to the pot and lower the heat to medium. Add the onions and hot pepper to the pot and sauté until onion is translucent, about 4 minutes. Add the garlic, cumin, caraway, and coriander to the pot and stir until fragrant, about 30 seconds. Add the chickpeas, some salt and black pepper to taste, and then stir to coat the chickpeas in spices. Add the tomatoes and vegetable stock to the pot.
Bring the braise to a boil and simmer, uncovered and stirring occasionally, for 10 minutes. Add the eggplant back into the pot and bring the braise up to a boil once more. Stir in the lemon juice and parsley. Serve the braised harissa eggplant hot over millet or rice (or any other starch of choice).