In a mixing bowl, combine softened cream cheese, pesto sauce, garlic powder, and parmesan cheese. Mix slowly until the texture becomes smooth and creamy with no lumps remaining. Make sure to scrape the sides of the bowl so everything is well combined.
Place the tortillas on a flat surface. Ensure they are soft and flexible. If they feel stiff, allow them to rest at room temperature for a few minutes before using.
Spread an even layer of the pesto cream cheese mixture over each tortilla. Use a spatula to gently push the mixture toward the edges while keeping the layer even and not too thick.
Sprinkle shredded mozzarella cheese evenly over each tortilla. Make sure the cheese is spread out so every bite has a good balance of flavor.
Starting from one side, roll each tortilla tightly into a log shape. Apply gentle pressure as you roll to keep the filling in place without squeezing it out.
Wrap each rolled tortilla in plastic wrap and place them in the refrigerator. Chill for at least 1 hour so the rolls firm up and hold their shape when sliced.
Remove the chilled rolls from the refrigerator and unwrap them. Using a sharp knife, slice each roll into even pieces. Clean the knife between cuts if needed to keep slices neat.
Arrange the pinwheels on a serving plate and serve immediately, or store in the refrigerator until ready to serve.