Place the eggplant in a colander set over a bowl or in the sink, and toss with 1 teaspoon of the salt. Allow to sit and drain for 30 minutes, then rinse the eggplant with cold water. Lay the eggplant on paper towels and pat with an additional paper towel to remove as much water as possible.
Whisk together the oil, tomato paste, the remaining 1/2 teaspoon of salt and the black pepper in a medium bowl until incorporated.
Combine the drained/rinsed eggplant, tomatoes, zucchini and/or squash, bell pepper, onion, garlic and thyme in your slow-cooker. Add the oil-tomato paste mixture and stir to incorporate. Add the bay leaf.
Cover and cook on LOW for 4 hours or until the vegetables are tender, then uncover and cook for 1 hour more to allow some of the liquid to evaporate and the vegetables to meld further. Discard the bay leaf.