Preheat oven to 425 degrees F.
Heat 1 tbsp olive oil in a large skillet over medium heat. Add half the chicken thighs to the skillet and sear for 2-3 minutes per side, until crisp. Transfer to sheet pan. Repeat with remaining chicken. Spread chicken out on the sheet pan about 2-3 inches from each other so they are not touching.
To make the balsamic vinaigrette. In a small bowl, combine balsamic vinegar, brown sugar, Italian seasoning, salt and pepper. Gradually whisk in 6 tbsp olive oil until the dressing is well combined.
In a large bowl, combine baby carrots, green beans, cherry tomatoes, and half of the balsamic vinaigrette. Toss together until well coated. Spread the veggies around the chicken in a single layer. Drizzle the remaining vinaigrette on the chicken thighs.
Place into oven and bake for 35-45 minutes until chicken is cooked through and veggies are tender. Remove from oven and garnish with basil ribbons.