Toss chicken (1 1/2 pounds) with 1/4 teaspoon salt, 1/2 teaspoon pepper, and Italian seasoning (1 tablespoon) and coat evenly.
Heat oil (2 tablespoons), over medium-high heat, in a large skillet. When the oil shimmers add chicken and cook for 3-4 minutes, stirring occasionally, or until it begins to brown. Transfer to a plate.
Stir in garlic (1 heaping tablespoon) and cook, stirring often, until fragrant, about 1 minute.
Add softened cream cheese (8 ounces), broth (1 cup), heavy cream (1 cup), onion powder (1/2 teaspoon), and nutmeg (1/4 teaspoon) then bring to a simmer.
Pour tortellini (19 ounces) into skillet and increase heat then bring to a boil. Immediately reduce heat and simmer, uncovered, until the tortellini is tender, and the sauce has thickened a bit, about 4 minutes.
Return the chicken and any juices that have accumulated on the plate. Add the Parmesan (1 1/2 cups) to the skillet then stir to combine, simmering for 1 minute, until the Parmesan melts. and chicken is heated through. Adjust seasoning if needed.
Remove from heat, sprinkle mozzarella (1 cup) over top of pasta, cover to allow mozzarella to melt. Sprinkle with green onions (1/4 cup) and serve.