Place the softened cream cheese in a medium mixing bowl.
Add the Dijon mustard, garlic powder, salt, and black pepper to the bowl.
Stir until the mixture is smooth and fully combined.
Lay one flour tortilla flat on a clean work surface.
Spread one-quarter of the cream cheese mixture evenly over the tortilla, leaving a 1/2-inch border around the edges.
Sprinkle one-quarter of the chopped turkey evenly over the cream cheese layer.
Add one-quarter of the chopped ham in an even layer.
Sprinkle one-quarter cup of shredded cheddar cheese over the meats.
Scatter a small handful of chopped spinach evenly across the surface.
Add one tablespoon of diced red bell pepper.
Press the fillings gently into the cream cheese to help them adhere.
Starting at one edge, roll the tortilla tightly into a firm log.
Wrap the rolled tortilla tightly in plastic wrap.
Repeat the process with the remaining tortillas and filling.
Place all wrapped rolls in the refrigerator for at least 1 hour to firm.
Remove one roll from the refrigerator and unwrap it.
Trim both ends with a sharp knife.
Slice the roll into 1-inch pinwheel pieces, wiping the knife clean between cuts.
Arrange the pinwheel sandwiches cut-side up on a serving platter and serve chilled.