In a medium bowl, combine the softened cream cheese, shredded cheddar cheese, diced ham, garlic powder, onion powder, salt, and pepper. Mix until well combined and smooth.
Lay one tortilla flat on a clean surface. Spread a generous layer of the ham and cheese mixture evenly over the tortilla, leaving a small border around the edges.
If using, sprinkle some 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 pinwheels. Arrange on a serving platter and enjoy!