Mix all of the ingredients in a small bowl, then brush the marinade over the eggplant slices. Bake on a baking sheet at 360°F/180°C for 20 minutes or a bit longer if needed, or shallow fry and pat dry on kitchen towel paper.
To Make the Sandwich:
Start by slicing the panini or ciabatta bread in half lengthwise.
Spread a layer of vegan mayonnaise, add a layer of smoky eggplant slices, followed by tomato slices, cucumber slices, a sprinkle of salt and pepper, and finally, top with rocket/arugula leaves and cover with the other half of the panini or ciabatta bread.
Cover with some foil, then toast the sandwich in a grill. Once you take it out, cut in halves (cut through the foil if you're going to have it right away. Or leave it packed in foil to take to work, a picnic or just have it later.