In a mixing bowl, combine the softened cream cheese, shredded cheddar cheese, diced ham, garlic powder, onion powder, and dried parsley. Mix until well combined and smooth.
Lay out a flour tortilla on a clean surface. Spread a generous layer of the cream cheese mixture evenly across the tortilla, leaving a small border around the edges.
Place a handful of fresh spinach leaves on top of the cream cheese mixture.
Starting from one end, tightly roll the tortilla 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!