Heat oil in a large stock pot or Dutch oven over medium heat. Once hot, add the onion, carrots, celery, and lemon peel. Cook for 10 minutes, stirring occasionally, until softened. Add garlic; cook 1 more minute, until aromatic.
Add broth and increase heat to bring mixture to a boil. Once boiling, add chickpeas, orzo, salt, pepper, and oregano. Simmer soup over medium-high heat, uncovered, for 10 minutes, or until the orzo is al dente. Reduce heat to low, and remove 3/4 cup hot broth from the soup. Set aside.
Place whole eggs, egg yolks, and lemon juice in a large bowl; whisk until combined. While whisking constantly, VERY slowly stream hot broth into egg mixture.*Note: It's easy to end up with scrambled eggs if you don't do this properly. When eggs are introduced to heat, they will immediately start to solidify, so to avoid this, you need to temper the eggs. This is achieved when you SLOWLY pour the hot broth into the eggs, while whisking constantly, which brings the eggs up to temperature without scrambling them.
While gently stirring the soup with a wooden spoon or ladle, stream the egg-broth mixture back into the pot of soup. Add kale and continue to cook over low heat for 5 minutes, or until the broth is slightly thickened and greens are wilted. Remove lemon peels.
Stir in fresh dill and taste/adjust seasonings as needed. Ladle soup into bowls and garnish with extra fresh dill, cracked black pepper, and a drizzle of olive oil, if desired.