Preheat the oven to 400°F (200°C).
Heat a large Dutch oven over medium-high heat and add 1/2 tablespoon of the olive oil until shimmering.
Pat the chicken thighs dry, season both sides with kosher salt and freshly ground black pepper, and place them skinless-side down in the hot pot. Cook without moving until browned and the meat releases, about 5 minutes.
Flip the thighs and brown the other side for about 3 minutes, then transfer the chicken to a plate and set aside.
Reduce heat to medium, add the remaining 1½ tablespoons olive oil, then add the chopped onion, minced garlic, and a pinch of salt. Cook, stirring occasionally, until softened, about 3 minutes.
Add the cubed eggplant and another pinch of salt. Cook, stirring occasionally, until the eggplant begins to soften, about 5 minutes.
Stir in the tomato paste and chopped thyme and cook, stirring constantly, for 1 minute to combine flavors.
Add the diced zucchini, bell pepper, and tomatoes, season with another pinch of salt and a twist of black pepper, and cook, stirring occasionally, until the vegetables are tender, about 10 minutes.
Remove the pot from the heat and nestle the browned chicken thighs partially into the vegetables.
Transfer the uncovered pot to the preheated oven and bake until the thickest part of the chicken reaches 160°F (71°C), about 20 minutes.
Remove from the oven and let the chicken rest in the pot for 10 minutes, then stir in the chopped basil and serve.