Meanwhile, melt the butter in a large nonstick skillet over medium-high heat. Add the chicken and ham; cook, stirring occasionally, until the chicken is almost cooked through, about 6 minutes. Add the garlic, onion, and mixed vegetables. Cook, stirring occasionally, until the vegetables are tender, about 4 minutes. Stir in the broth, thyme, and pepper; cook 2 minutes.
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Blend the cornstarch with the milk in a small bowl, and stir into the skillet. Bring the mixture to a boil and cook, stirring constantly until thickened, about 1 minute. Top the skillet with the biscuits and serve.
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