In a small bowl, combine the oregano, sugar substitute, garlic powder, onion powder, basil, parsley, tarragon, thyme, salt, and pepper.
Whisk together to eliminate lumps. You should have a total of about 3 tablespoons of seasoning mix.
Divide seasoning mix: Set aside 2 tablespoons for the marinade and 1 tablespoon for the sauce.
Marinate The Chicken:
In a large measuring cup, whisk together the oil, balsamic vinegar, water, and 2 tablespoons of the seasoning mix.
Place the chicken breasts in a single layer in a 9x13-inch baking dish.
Pour the marinade over the chicken, turning the pieces to coat well.
Cover tightly and refrigerate for at least 30 minutes, or up to 2 hours for more flavor.
Bake The Chicken:
Preheat oven to 400°F. Move oven rack to center position.
Remove baking dish from refrigerator and uncover. Do not drain the marinade.
Bake the chicken in the marinade for 30-35 minutes, until chicken is golden around the edges, juices run clear, and the internal temperature reaches 165°F.
Let chicken rest in the baking dish, loosely covered, for 5 minutes.
Make The Sauce:
In a nonstick skillet over medium heat, melt the butter.
Add the garlic and shallots and sauté until softened and aromatic, about 1-2 minutes.
Add the halved tomatoes to the skillet. Sauté until tomatoes begin to blister and pop, about 2-3 minutes.
Sprinkle in the remaining 1 tablespoon of seasoning mix. Cook and stir for 1-2 minutes.
Pour in the balsamic vinegar, then the heavy cream, stirring constantly. Cook until sauce thickens slightly, about 2-3 minutes.
Assemble And Serve The Dish:
Use a slotted spoon to transfer the baked chicken to a serving dish or plate. Discard the marinade.
Spoon warm cream sauce evenly over each chicken breast. Serve immediately.