Preheat oven to 400 degrees F (200 degrees C). Grease a baking sheet with 1 teaspoon olive oil.
Place eggplant in a large bowl. Drizzle 1/4 cup olive oil over eggplant and toss to coat. Spread eggplant on the prepared baking sheet.
Bake in the preheated oven, stirring occasionally, until eggplant is softened and browned, about 25 minutes. Season with salt and pepper.
Heat 2 tablespoons olive oil in a large, wide pot over medium-high heat; cook and stir onions and garlic until onions are softened, about 10 minutes. Stir paprika, kosher salt, coriander, fennel seeds, black pepper, cumin, ginger, and turmeric into onion mixture; cook and stir for 1 minute.
Mix tomatoes, half of the reserved tomato juice, red bell peppers, white wine, and lemon juice into onion mixture; bring to a boil. Reserve the remaining tomato juice to thin the stew if needed.
Arrange chicken in a single layer in the pot; cover with some of the tomato mixture. Return stew to a boil; reduce heat to medium-low, cover, and simmer for 15 minutes. Flip chicken, cover, and simmer until no longer pink in the center, about 20 minutes. An instant-read thermometer inserted into the thickest part of the thigh, near the bone, should read 165 degrees F (74 degrees C).
Stir eggplant and marjoram into stew; simmer uncovered until heated through, about 10 minutes.