Wash and dry the vegetables thoroughly. Finely dice the cucumber, red bell pepper, and carrots.

Pat the cucumber dry with paper towels if it is especially watery.

In a medium bowl, combine the softened cream cheese, Greek yogurt, onion powder, dried parsley, salt, and black pepper. Stir until smooth and creamy.

Warm each tortilla in the microwave for about 15 seconds, just until soft and flexible.

Lay one tortilla flat on a clean work surface and spread half of the cream cheese mixture evenly over the surface, leaving a small border around the edge.

Sprinkle half of the chopped vegetables, Monterey Jack cheese, and chives evenly over the filling.

Repeat with the second tortilla and the remaining filling ingredients.

Starting from one edge, roll each tortilla tightly without squeezing out the filling. Place the rolls seam-side down.

Wrap each roll tightly in plastic wrap or place in an airtight container and refrigerate for at least 30 minutes.

Remove the chilled rolls from the refrigerator, trim the uneven ends, and slice each roll into 3/4- to 1-inch pieces.

Arrange the pinwheels on a platter and serve chilled.