Preheat the oven to 425 degrees F.
Heat the heavy cream, butter, nutmeg, 1 cup of the Parmesan and 1 teaspoon salt in a large ovenproof skillet over medium-high heat, whisking occasionally, until the cheese and butter are melted, 3 to 4 minutes. Add the tortellini and simmer until cooked through, 4 to 5 minutes. Add the chicken and sprinkle with the remaining 1/2 cup Parmesan.
Bake until the chicken is just cooked through, the sauce has thickened and the top starts to turn golden brown, 10 to 12 minutes. Let stand for 10 minutes before serving. Sprinkle with the parsley.
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