Yatimcheh Iranian Eggplant Tomato Potato Stew

Name: Yatimcheh (Iranian Eggplant, Tomato & Potato Stew)
Ingredients: 1 large eggplant (about 1 1/4 pounds; see Tips), peeled and cubed (1-inch); ½ cup olive oil, divided; 1 ½ teaspoons kosher salt, divided (see Tips); 1 medium yellow onion, finely chopped; 2 cloves garlic, crushed to a paste (see Tips); ½ teaspoon ground turmeric; 1 large Yukon Gold potato (about 8 ounces), diced (1/2-inch); 2 large tomatoes (about 10 ounces), diced (1/2-inch); ¾ cup water, as needed; ¼ teaspoon ground pepper