Whisk together the mayo, olive oil, lemon juice, and garlic. Set this aside for later in the recipe.
Step 2
Use a vegetable peeler to peel wide and flat strips away from a whole cucumber, amounting the to weight listed in the ingredients. Arrange them parallel to each other, one slightly overlapping the next, into a rectangle shape (about 8×6 inches). Use paper towels to press into the cucumber and soak up all excess moisture.
Step 3
On top of the cucumber strips, arrange a layer of salami slices, followed by pepperoni, followed by capicola. Leave about 1-inch of bare cucumber at the top and bottom of your rectangle. Arrange small leaves of basil across the center.
Step 4
Starting from the bottom of the rectangle, roll the cucumber strips up into a tight roll. Your finished roll will look like a sushi roll filled with Italian meats! Slice the roll into 6 pieces and drizzle the garlic aioli over the tops of the pieces or serve on the side.