Preheat your oven to 375°F (190°C) and line a baking sheet with parchment paper.
In a mixing bowl, combine the softened cream cheese, shredded cheddar cheese, diced ham, garlic powder, onion powder, black pepper, and paprika. Mix until well combined.
Lay out one tortilla 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 this process with the remaining tortillas and filling.
Once all tortillas are rolled, slice each log into 1-inch thick pinwheels.
Place the pinwheels on the prepared baking sheet, cut side up. Sprinkle the shredded mozzarella cheese on top of each pinwheel.
Bake in the preheated oven for 15-20 minutes, or until the cheese is melted and the pinwheels are golden brown.
Remove from the oven and let cool for a few minutes before serving.