To a large mixing bowl, add the cream cheese, oregano, garlic powder, and cumin. Use a spoon or spatula to mix everything together until evenly combined.
Add the cheese, chicken, and salsa to the cream cheese mixture. Stir together until evenly combined.
Add the cilantro and bell peppers to the filling. Stir until incorporated.
Lay one tortilla flat on a cutting board. Place 1/3 of the filling in the center of the tortilla. Use the back of a spoon or a spatula to spread the filling evenly over the tortilla. (You don't need to go all the way to the sides as they will be discarded later.) Carefully roll up the tortilla, starting with the side closest to you, until you create a log shape.
Repeat filling and rolling the remaining two tortillas, using 1/3 of the filling for each.
Use a sharp knife to cut the end off of one of the rolled tortillas so that your next cut is where the filling starts. Cut the tortilla into 1/4-inch to 1/2-inch slices. (You should get about 8 pinwheels per tortillas.)
Place the pinwheels on a serving plate.
Serve immediately, or cover with plastic wrap and refrigerate until ready to serve.
Video
Notes
The number of pinwheels will vary based on the size of your tortillas, the amount of filling used, and how thick you cut the slices.
You can cut down on the prep time by using store-bought rotisserie chicken or using left oven chicken from dinner the night before.