In a large mixing bowl, combine shredded chicken, softened cream cheese, shredded cheddar cheese, ranch seasoning mix, crumbled bacon, and chopped green onions. Mix thoroughly until all ingredients are well combined and the mixture is creamy and uniform, about 2 minutes.

Lay one flour tortilla flat on a clean work surface. If tortillas are cold, let them sit at room temperature for 5 minutes to prevent cracking. Spoon about 1/2 cup of the chicken mixture onto the center and spread it evenly across the entire tortilla surface, leaving about a half-inch border around the edges.

Starting at one end, roll the tortilla tightly, keeping even pressure to prevent filling from squeezing out. The tighter the roll, the better your pinwheels will look when sliced. Repeat with remaining tortillas and filling.

Wrap each rolled tortilla individually in plastic wrap and refrigerate for at least 30 minutes to firm up the filling. For best results or make-ahead convenience, chill up to 24 hours.

Once chilled, unwrap the rolls and use a sharp serrated knife to slice each one into 1-inch thick pinwheels. Wipe the knife clean between cuts for neatest presentation. You should get about 8 pinwheels per tortilla roll.

Arrange pinwheels on a serving platter cut side up. Garnish with fresh parsley if desired. Let sit at room temperature for 10-15 minutes before serving for best flavor.