Slice the eggplant into thin rings and assemble them in a single layer on a baking sheet. Drizzle olive oil over them, followed by a sprinkle of salt and pepper.
Broil the eggplant until they are soft and slightly browned. Flip them over and brown the other side.
Remove eggplant from oven and let them cool to room temperature.
In a small bowl, mix the mayonnaise and crushed garlic.
Arrange the eggplant slices on a serving plate. Spread a thin layer of the garlicky mayo on top of each, followed by a tomato slice and a little dollop of the mayo. Garnish with dill and serve immediately.