Cut a 2 to 3-inch pocket in each chicken breast, and insert a wedge of Brie deep into each pocket and is covered with the top of the pocket.
In a large mixing bowl, add all the dried herbs and spices. Add the chicken and gently toss the in the mixture, coating evenly (keeping the cheese in the pocket). In a large skillet over high heat, add oil and sear the chicken on both sides until dark brown, but not burned, normally 3 to 4 minutes on each side. Put the skillet in the oven to bake until cooked through, about 6 to 8 minutes. Remove the chicken from the oven to a cutting board and let rest for 3 to 4 minutes.
For the salad:
Dice the heirloom tomatoes and add them to a large mixing bowl. Stir in the next 4 ingredients. Toss to combine and add the fresh basil just before serving.
Slice the chicken and arrange on a serving platter. Serve with the tomato salad.