Pat dry 6 chicken thighs and season with 1 ½ teaspoons of the kosher salt and ½ teaspoon of the black pepper.
Heat 3 tablespoons olive oil in a 12-inch skillet or large Dutch oven over medium-high until shimmering. Sear the chicken in batches if needed so as not to crowd the pan: Place the chicken skin-side down in the skillet and cook until browned on the bottom, 8 to 9 minutes. Reduce the heat to medium. Flip the chicken and cook until the second side is browned, about 10 minutes. Transfer the chicken to a plate.
While the chicken is cooking, thinly slice 1 small shallot (about 3 tablespoons) and mince 4 garlic cloves (about 2 tablespoons). Cut 1 large eggplant into 1-inch cubes (about 7 cups).
Once the chicken is browned, add the shallots to the skillet. Cook over medium heat, scraping up the browned bits from the bottom of the pan with a wooden spoon, until the shallots are translucent, 1 to 2 minutes. Add the garlic and cook until fragrant, about 1 minute. Add 1 tablespoon tomato paste, 1 teaspoon ground turmeric, ½ teaspoon cayenne pepper, the remaining 1 teaspoon kosher salt, and remaining ¼ teaspoon black pepper. Cook, stirring frequently, until the tomato paste darkens in color, about 2 minutes.
Add the eggplant, 1 (14.5-ounce) can crushed tomatoes, and 1 cup low-sodium broth. Stir to combine and bring to a simmer.
Add 1 ½ cups pearl couscous and stir until thoroughly combined. Return the chicken skin-side up to the pan, nestling it into the couscous mixture, and add any accumulated juices from the plate. Cover with a lid or aluminum foil and cook undisturbed until the couscous is al dente, about 15 minutes. Remove from the heat and let rest covered for 5 minutes. Coarsely chop 5 fresh basil leaves and sprinkle on the chicken and couscous before serving.
