In a small bowl, mash the avocado with the pressed garlic and lime juice until smooth. Season with sea salt and freshly ground black pepper to taste.

Using a vegetable peeler or mandoline, slice the cucumbers lengthwise into thin strips.

Lay out a cucumber slice and spread a thin layer of the avocado mixture on top.

Place a slice of turkey or ham on the avocado layer, followed by a slice of cheese.

Roll the cucumber slice tightly from one end to the other, securing with a toothpick if needed.

Repeat with the remaining cucumber slices, turkey, and cheese.

Garnish with fresh chopped parsley and serve immediately.