Wash the cucumbers and cut them lengthwise into long, thin strips using a mandoline slicer or vegetable peeler. Pat dry with paper towels.
Combine tuna, mayonnaise, Greek yogurt, Dijon mustard, lemon juice, salt, and black pepper in a bowl until creamy.
Overlap the cucumber strips on a flat surface to form a rectangle. Spread the tuna mixture evenly over the cucumber and top with avocado and shredded carrot.
Roll tightly like sushi, slice into bite-sized pieces, and garnish with sesame seeds. Serve immediately or chill before serving.