Grate the broccoli with a cheese grater to make broccoli rice. Set aside.
- Finely chop the onion and mince the garlic. Dice the chicken.
Heat the olive oil in a saucepan and sauté the chicken with the onions for 5 minutes, then add the broccoli, the rice and minced garlic and cook for another minute to combine the flavors. Gradually add the broth to deglaze the saucepan and simmer for 15 minutes, adding broth or water as needed.
- Whisk the egg yolks with the lemon juice.
- Remove the soup from the heat and while still hot stir in the egg yolk mixture, whisking gently to incorporate to the soup. Serve hot, topped with crumbled feta cheese.