Preheat oven to 400°F (200°C). Halve eggplants lengthwise and scoop out flesh, leaving a 1/2-inch border. Finely chop the flesh. Season shells with black pepper and the remaining 1/4 teaspoon kosher salt.
Heat olive oil in a large oven-safe braiser or skillet over medium-high. Sauté onion 4–5 minutes until softened. Add garlic; cook 1 minute.
Add turkey (or lentils); cook, breaking up, until turkey is browned, 5–7 minutes. Stir in chopped eggplant flesh; cook 3–4 minutes until starting to soften.
Add tomatoes, 1/2 teaspoon kosher salt, cumin, allspice, coriander, oregano, smoked paprika, and red pepper flakes. Stir, cover, reduce heat, and simmer 5 minutes.
Transfer mixture to a bowl. Stir in rice, herbs, 2 tablespoons pine nuts, and red wine vinegar. Adjust seasoning to taste.
In the empty skillet, whisk broth with tomato paste, smoked paprika, and oregano. Bring to a gentle simmer, scraping up browned bits; season to taste with pepper (add a pinch of salt if needed), then turn off heat.
Mound filling into eggplant shells. Nestle stuffed halves into the tomato broth; broth should come 1/4–1/2 inch up the sides.
Cover tightly and bake 40–45 minutes, until eggplant is fork-tender and the center of the turkey filling reaches 165°F (74°C). Uncover and bake 5–10 minutes to lightly brown. Garnish with remaining herbs and the last tablespoon of pine nuts.