Slice each chicken breast in half horizontally to create 4 thinner cutlets. Pat the chicken dry and season both sides with salt and pepper.
Heat the olive oil in a large skillet over medium heat. Add the chicken and sear for 4 to 5 minutes per side, or until cooked through to an internal temperature of 165°F. Transfer the chicken to a plate and set aside.
To the same skillet, add the butter and garlic. Cook for about 1 minute, stirring often.
Add the chicken broth, balsamic vinegar, honey, Dijon mustard, Worcestershire sauce, and dried basil. Stir, scraping up any browned bits from the bottom of the skillet. Bring to a simmer.
In a small bowl, whisk together the cornstarch and cold water to make a slurry. Stir the slurry into the simmering sauce. Cook for 1 to 2 minutes, stirring, until the sauce thickens slightly and looks glossy.
Add the peach slices and cook for 2 to 3 minutes, gently stirring, until the peaches begin to soften but still hold their shape.
Return the chicken to the skillet and spoon the sauce and peaches over the top. Cook for about 2 minutes, or until the chicken is heated through.
Add salt to taste. Serve topped with toasted pecans and fresh thyme, if using.