Place the olive oil in a blender with the fresh basil and a pinch of salt. Blend until smooth, then pour into a small container and set aside.
Place the ciliegine “cherry sized” mozzarella balls on a cutting board. Look at each one and determine the best side to be the “top”, the top should be slightly rounded and wide. Slice small amounts of the “bottom” to make sure it sits flat on the table if needed. Use a sharp paring knife to cut a small circle in the top of the mozzarella balls, but do not cut all the way through to the bottom, only cut about ¼” or less deep. This circle will be the “iris” of the eyeball, it should be larger than the opening of a wide mouthed straw, but small enough that you can see plenty of the white of the mozzarella around it. Set aside.
Slice each of the black olives in half, lengthwise. With the inside of the halved olive facing up, use a wide mouth straw to punch a hole in the middle of the olive, just like a cookie cutter. Save the small circle of olive and discard the rest, this will become the “pupil” of the eyeball.
To assemble. Use a small spoon to stir the basil oil, then fill each of the holes in the mozzarella balls with the basil oil, filling them almost to the top.
Place one of the olive “pupils” smooth side up in the center of the basil oil in the mozzarella balls. Add additional basil oil if needed to fill the cavity in the mozzarella ball to the top.
Take one of the thin slices of deli ham and fold in half lengthwise. Wrap the outside of the mozzarella ball with the ham, add additional pieces as needed. Form the ham so that it is in an eye shape.
Crumple up a sheet of brown parchment paper, the size of your serving platter, then uncrumple it and place it onto your serving platter.
Drizzle the balsamic glaze in a few lines on the wrinkled parchment, then smear around with a spoon. Place sundried tomatoes all around on top of the glaze and sprinkle with flake salt.
Arrange the eyeballs on top of the sun dried tomatoes.