On a cutting board use a sharp knife to cut the ham into small pieces. Save until Step 3.
Cook tortellini in a large saucepan following the package directions, adding the broccoli with the pasta so they cook at the same time. Turn off the burner. Remove saucepan from burner. Place a colander in sink. Carefully pour tortellini mixture into the colander to drain.
Add the butter to the empty saucepan. Put the saucepan on a burner. Turn burner to medium-low heat. Cook about 20 seconds or until butter is melted. Carefully add the garlic. Cook for 30 seconds, stirring with the wooden spoon. Use a rubber scraper to remove half of the cream cheese from the tub and carefully add to the saucepan. Save remaining cream cheese for another use. Add milk to the saucepan. Use a wire whisk to stir until mixture is smooth. Stir in the ham and pepper. Cook and stir for 2 minutes more. Turn off burner. Remove saucepan from burner.
Add the tortellini mixture to the ham mixture in the saucepan. Using the wooden spoon, gently stir until combined. Pass Parmesan cheese to sprinkle over the tortellini.
Serve with breadsticks, sherbet for dessert, and milk.