In a medium bowl, mix together the softened cream cheese, sour cream, Dijon mustard, honey, garlic powder, and black pepper until smooth and well combined.
Lay out one tortilla on a clean work surface. Spread about 3-4 tablespoons of the cream cheese mixture evenly over the entire tortilla, going all the way to the edges.
Layer about 3-4 slices of ham over the cream cheese, covering the surface completely.
Sprinkle about 1/4 cup of shredded cheese over the ham, then add a thin layer of spinach leaves.
Starting from one end, tightly roll up the tortilla like a jelly roll. Make sure it's snug but not so tight that the filling squeezes out.
Wrap the rolled tortilla tightly in plastic wrap and repeat with remaining tortillas and filling.
Refrigerate the wrapped rolls for at least 2 hours or overnight to firm up, which makes slicing much easier.
When ready to serve, unwrap each roll and trim off the ends. Slice each roll into 1-inch thick pinwheels using a sharp knife. Arrange on a festive platter and serve chilled!