In a medium mixing bowl, combine the cream cheese, sour cream, salsa, and fajita seasoning. Use a whisk or spatula to blend the ingredients until smooth and well combined. This mixture will be the flavorful base of your pinwheels.

Lay out the tortillas on a clean, flat surface. Divide the cream cheese mixture evenly among the four tortillas. Use a butter knife or spatula to spread the mixture across each tortilla in an even layer, leaving about a ½-inch border around the edges to prevent overflow.

Sprinkle the green chilies, shredded cheese, and sliced black olives evenly over the tortillas. Be sure to distribute these ingredients uniformly so that every bite is packed with flavor.

Starting at one edge of a tortilla, carefully roll it tightly into a log, ensuring the filling and toppings stay in place. Roll with consistent pressure to create a firm and compact pinwheel. Repeat this step for all the tortillas.

Wrap each rolled tortilla tightly in plastic wrap to help it maintain its shape. Place the wrapped rolls in the refrigerator and chill for at least 1 hour. This step allows the filling to firm up, making the pinwheels easier to slice and serve.

Remove the chilled tortilla rolls from the refrigerator and unwrap them. Using a sharp knife, trim about 1 inch off each end of the rolls to remove any uneven sections (feel free to snack on these!). Then, slice the remaining roll into 1-inch pieces to create pinwheels.

Lay the pinwheels flat on a serving platter, showcasing their colorful, layered appearance. Serve immediately and enjoy these cheesy, zesty bites that are perfect for any gathering!