Place a rimmed baking sheet in the oven and preheat to 450 degrees F. Brush the cut sides of the eggplants with 2 tablespoons olive oil and season with salt and pepper. Place cut-side down on the hot baking sheet and roast until tender, about 25 minutes.
Meanwhile, heat 2 tablespoons olive oil in a large nonstick skillet over medium-high heat. Add the panko and smashed garlic; season with salt and pepper. Cook, stirring, until toasted, 2 to 3 minutes. Transfer to a bowl; stir in the cheese and half the parsley. Discard the garlic.
Wipe out the skillet; add the remaining 2 tablespoons olive oil and heat over medium-high heat. Add the onion, minced garlic, herbes de Provence and 1/4 teaspoon salt; cook, stirring, until softened, 5 minutes. Add the turkey, 3/4 teaspoon salt and a few grinds of pepper; cook, breaking up the meat, until lightly browned, about 4 minutes. Add the tomatoes and simmer until thickened, about 5 minutes. Stir in the quinoa and remaining parsley. Cook until hot, 1 to 2 minutes.
Scoop out most of the flesh from each eggplant, leaving a shell. Roughly chop the flesh and stir into the turkey mixture. Stuff the eggplant shells with the turkey mixture and top with the toasted panko. Drizzle with olive oil.