Bring a large pot of salted water to a boil. Cook the tortellini according to package directions until al dente. Reserve 2–4 tablespoons of the cooking water, then drain the pasta.

While the pasta cooks, heat butter or oil in a large skillet over medium heat.

Add the diced ham and sauté 1½–2 minutes, just until heated through and slightly browned at the edges.

Pour in 1/2 cup of the chicken broth and the heavy cream. Reduce heat to low and bring the mixture to a gentle simmer. Season lightly with salt and pepper.

Remove the skillet briefly from the heat. Stir in the grated parmesan a handful at a time until melted and the sauce becomes slightly thickened and glossy. If the sauce tightens too much, add more broth a tablespoon at a time.

Add the drained tortellini to the skillet and toss gently to coat. If the sauce feels too thick, stir in reserved pasta water or additional broth until the consistency is saucy and smooth.

Taste and adjust seasoning. Serve immediately with extra parmesan and a sprinkle of chopped parsley.