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Preheat the oven to 425°F.
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Spray a large baking dish or sheet pan with nonstick cooking spray. Butterfly cut each chicken breast.
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On one side of the chicken, lay 7-8 thin apple slices followed by 4-5 slices of cheese. Sprinkle with 1/2 teaspoon fresh thyme. Fold over and drizzle with 1/2 teaspoon olive oil. Sprinkle with 1/4 teaspoon salt and 1/4 teaspoon pepper.
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Place the chicken breast on sheet pan and top with another sprig of fresh thyme if desired.
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In a bowl, mix diced sweet potatoes with olive oil, smoked paprika, 1 teaspoon thyme leaves and sea salt until evenly coated. Arrange sweet potatoes in a single layer around chicken breasts.
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Bake for 20 minutes, remove from oven, and stir sweet potatoes.
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Continue to bake until the juices run clear from chicken and internal temperature of chicken registers at 165°F, about 10 additional minutes. Sweet potatoes should be fork tender.