Heat the olive oil in a large pot over medium heat. Add the minced garlic and cook for one minute until fragrant.
Pour in the vegetable broth and bring it to a boil. Stir in the orzo and cook for 8 minutes.
Add the chopped escarole to the pot. Simmer for 3 to 4 minutes until the greens wilt.
In a medium bowl, whisk the eggs with the lemon juice until smooth.
Ladle about one cup of hot broth into the egg mixture while whisking constantly to temper the eggs.
Slowly pour the tempered egg mixture back into the pot while stirring. Keep the heat on low and do not let the soup boil.
Season with salt and black pepper. Stir in the fresh dill just before serving.