Start by preparing your cream cheese mixture, which is really the heart of these pinwheels. In a medium mixing bowl, combine the softened cream cheese and sour cream, beating them together until you get a smooth, creamy consistency.
Add the Dijon mustard, garlic powder, black pepper, and paprika to your cream cheese mixture, stirring everything together until well combined.
Fold in the shredded cheddar cheese and chopped fresh chives.
Lay your tortillas flat on a clean work surface. Using a spatula or butter knife, spread about 1/4 of the cream cheese mixture evenly over each tortilla, making sure to spread it all the way to the edges.
Layer 2-3 slices of deli ham over the cream cheese on each tortilla, covering the surface evenly.
Now comes the rolling part. Starting from one edge, tightly roll up each tortilla like a jelly roll or burrito.
Refrigerate the wrapped tortilla rolls for at least 2 hours, though overnight is even better.
When you’re ready to serve, unwrap the chilled rolls and place them on a cutting board. Using a sharp serrated knife, trim off the uneven ends, then slice each roll into 1/2 to 3/4-inch thick rounds.