In a medium mixing bowl, combine the cream cheese, cheddar cheese, mayonnaise, chopped chives, Dijon mustard, salt, black pepper, and garlic powder. Blend until smooth and creamy, about 3-5 minutes.

Lay one burrito-sized tortilla flat on a clean surface and spread 1/4 of the cheese mixture over it, leaving a short border around the edges.

Place two slices of smoked ham in the center of the tortilla, followed by a few leaves of green leaf lettuce.

Starting from one edge, gently roll the tortilla away from you, enclosing the filling and lettuce tightly.

Once rolled, place each seam-side down on a plate and repeat with remaining tortillas and filling.

Cover the roll ups with plastic wrap or aluminum foil and refrigerate for 30 minutes to 1 hour.

Trim the ends of each roll and slice into bite-sized pieces, about 1 inch thick, and arrange them on a platter.