Season the chicken thighs with salt, pepper, Italian seasoning, oregano, and dried basil. Heat the skillet with some olive oil and sear the chicken for 3-5 minutes per side until golden brown. Remove and set aside.
Add the remaining olive oil to the skillet, then sauté garlic for about 30 seconds until fragrant. Toss in onions, bell peppers, and cherry tomatoes, seasoning with a pinch of salt and reserved herbs. Cook until soft, around 7-10 minutes.
Stir in giardiniera and fresh basil, letting it heat through. Return the chicken to the skillet, nestling it among the veggies.
Sprinkle the chicken with Parmesan and top with mozzarella slices. Broil for 3-5 minutes until the cheese bubbles and turns golden. Garnish with extra basil and remaining giardiniera before serving.