1. Remove the leaves from the celery branches and cut the branches into 1/2-inch (1,25cm) thick slices. Bring a medium sized pot of water to a low boil and simmer the celery until crisp-tender, about 5 to 7 minutes. Drain and rinse well in cold water. Set aside.
2. Trim the stems off eggplant and cut into 1-inch (3cm) pieces.
3. In a large, heavy-duty skillet (I used cast iron) heat 3/4-inch (2cm) of vegetable or olive oil. Cook the eggplant in batches, not crowding too many into the pan at once, turning them occasionally, until they are browned all over. Remove with a slotted spoon and drain on a baking sheet lined with paper towels. Season with salt, then fry the rest of the eggplant in batches, seasoning them with salt as you remove them from the oil. You’ll likely need to add more oil to the pan as you go. (I ended up using a total of 1 cup/250ml.)
4. In a large skillet or Dutch oven, heat the olive oil. Add the onion and cook, stirring frequently until wilted and starting to turn golden brown, 5 to 7 minutes. Add the parboiled celery, olives, capers, tomato sauce, vinegar, honey, and red pepper flakes. Let come to a low boil then add the eggplant.
5. Cook the mixture at a simmer, stirring carefully so as not to mash up the eggplant pieces, for 3 to 4 minutes. Taste, and add additional salt if desired, and perhaps another splash of vinegar. Remove from heat and transfer the caponata to a large, shallow serving platter or bowl and cool.