Spread the hummus evenly across a large serving board in a thick, round layer.
Mix the tahini with water in a small bowl until it reaches a pourable consistency.
Spoon the thinned tahini into a zip-top bag and snip a small corner. Pipe four concentric circles on top of the hummus.
Drag a toothpick from the center outward through the circles at even intervals to form a web pattern.
Slice four black olives in half and place them on the web to resemble spiders.
Arrange the salami slices, cheddar cubes, carrot sticks, cucumber slices, and crackers around the hummus in separate sections.
Sprinkle the chopped parsley over the vegetables and cheese for color.