In a bowl, mix the softened cream cheese with chopped chives, parsley, salt, and black pepper until well combined.
Spread an even layer of the cream cheese mixture over each flour tortilla.
Sprinkle the finely diced smoked salmon evenly over the cream cheese layer on each tortilla.
Carefully roll up each tortilla tightly into a log shape.
Using a sharp knife, slice each rolled tortilla into 1-inch pinwheel pieces.
Arrange the pinwheels in a circular pattern on a white round plate for a clean and minimalistic presentation.