Prepare the Chicken: Using a sharp chef's knife, carefully slice each chicken breast in half horizontally to create 4 thinner cutlets of even thickness.
Season both sides of the chicken cutlets with the garlic powder, salt, and pepper. Place about ¼ cup of all purpose flour in a shallow dish. Dredge each cutlet lightly in the flour, shaking off any excess.
Sear the Chicken: Heat the olive oil and butter in a large skillet over medium high heat. Once the butter has melted and the pan is hot, carefully add the chicken cutlets in a single layer (you may need to do this in batches to avoid crowding the pan).
Cook for 4-5 minutes per side, until the chicken is deeply golden brown and cooked through. Transfer the cooked chicken to a plate and set aside. Remove the skillet from the heat momentarily.
Build the Sauce: Return the skillet to medium heat. Add the minced garlic, Dijon mustard, and chicken broth. Stir immediately, using a wooden spoon to scrape up any browned bits (fond) from the bottom of the skillet.
Let the mixture bubble and cook for about 30-60 seconds, or until the garlic is fragrant and the liquid has slightly reduced.
Reduce the heat to medium low. Pour in the heavy cream, then add the chopped tomato, Italian seasoning, and the chopped fresh basil. Stir to combine.
Simmer and Finish: Bring the sauce to a gentle simmer. Once bubbling, return the chicken cutlets to the skillet, nestling them into the sauce.
Cook for an additional 3-5 minutes, or until the chicken is heated through and the sauce has slightly thickened to your liking. If the sauce is bubbling too vigorously, reduce the heat to low.
Taste the sauce and adjust seasoning with additional salt and pepper, if needed. Serve immediately.