Preheat the oven to 400°F (200°C).
Pat the chicken thighs dry with paper towels. Season both sides with kosher salt and black pepper.
In a food processor, combine the basil leaves, Parmesan cheese, pine nuts, and garlic cloves. Pulse until finely chopped.
With the processor running, slowly drizzle in the 1/3 cup extra-virgin olive oil until the mixture forms a smooth pesto. Set aside.
Heat 2 tablespoons olive oil in a large oven-safe skillet over medium-high heat.
Add the chicken thighs skin-side down and sear for 5-6 minutes until the skin is golden brown and crispy.
Flip the chicken thighs and cook for an additional 2 minutes on the other side.
Remove the skillet from heat. Spread about 2 tablespoons of pesto evenly over each chicken thigh.
Transfer the skillet to the preheated oven and bake for 25-30 minutes, or until the chicken reaches an internal temperature of 165°F (74°C).
Remove from the oven and let the chicken rest for 5 minutes before serving.