Pound chicken breasts to an even thickness, then season both sides with salt and black pepper.
In a large skillet over medium-high heat, add 2 tablespoons olive oil. When hot, add the seasoned chicken breasts.
Cook for 5-6 minutes on each side, or until the internal temperature of the chicken reaches 165 degrees Fahrenheit.
Remove the chicken from the skillet and set aside.
In the same skillet over medium heat, add the butter. Once the butter has melted, add the diced apples and shallot and sauté for 3-5 minutes, or until the apples and shallots are tender.
Pour in the apple cider, scraping up any browned bits from the bottom.
Allow the mixture to simmer for 5-7 minutes, or until it has reduced by half.
In a small bowl combine 1 tablespoon cold water with 1 tablespoon cornstarch. Stir to combine then whisk into sauce.
Stir in Dijon mustard and brown sugar. Heat for an additional 3-5 minutes to allow the sauce to thicken slightly.
Adjust salt to taste.
Return the chicken to the pan and heat for a minute or two.
Plate the chicken and spoon the apple cider sauce over the top.
Garnish with chopped fresh rosemary.