Heat the olive oil in a large pot over medium heat. Add the onion and garlic and cook for 3 minutes until the onion softens.
Stir in the eggplant cubes and cook for 6 to 7 minutes, stirring occasionally, until the edges begin to brown.
Pour in the vegetable broth, then add the gigante beans and oregano. Bring the mixture to a simmer and cook for 15 minutes.
In a medium bowl, whisk the eggs with the lemon juice until smooth. Slowly ladle about 1 cup of hot broth from the pot into the bowl while whisking constantly to temper the eggs.
Reduce the heat to low and pour the tempered egg mixture back into the pot while stirring. Cook for 2 minutes more without boiling. Season with salt and black pepper.
Ladle the soup into bowls and top each serving with fresh dill.