In a medium bowl, combine the softened cream cheese, shredded cheddar cheese, diced ham, garlic powder, onion powder, and black pepper. Mix until well combined and creamy.
Lay a tortilla flat on a clean surface. Spread a generous layer of the cheese and ham mixture evenly over the tortilla, leaving a small border around the edges.
If using, sprinkle a little chopped parsley over the cheese mixture for added flavor and color.
Starting from one edge, carefully roll the tortilla tightly into a log shape. Repeat with the remaining tortillas and filling.
Once all tortillas are rolled, wrap each log in plastic wrap and refrigerate for at least 30 minutes to firm up.
After chilling, remove the plastic wrap and slice each log into 1-inch thick pinwheels. Arrange on a serving platter and enjoy.