In a bowl, mix the softened cream cheese with chopped fresh chives and parsley until evenly combined.
Lay out one flour tortilla on a clean surface.
Spread a generous layer of the cream cheese and herb mixture evenly over the tortilla.
Place one slice of deli ham on top of the cream cheese layer.
Roll the tortilla tightly from one edge to the other to form a log.
Repeat with remaining tortillas and ingredients.
Using a sharp knife, slice each rolled tortilla into 1-inch pinwheel shapes.
Arrange the pinwheels in a circular pattern on a white plate, ensuring herb specks are visible for a clean, neat presentation.