In a medium mixing bowl, combine cream cheese, shredded cheddar, mayonnaise, chopped chives, Dijon mustard, salt, black pepper, and garlic powder. Mix until smooth and creamy.

Lay one burrito-sized wrap flat on a clean cutting board. Spread 1/4 of the cheese mixture evenly over the wrap, leaving a small border.

Place 2 slices of ham horizontally in the center of the wrap followed by a layer of lettuce.

Starting from one edge, roll the wrap tightly into a log shape, keeping the ingredients snug.

Place seam-side down on a plate and repeat with remaining wraps and filling.

Cover with plastic wrap and refrigerate for 30 minutes to 1 hour.

Trim the ends of each roll and slice into 8 even pieces. Arrange on a platter.