In a large skillet, heat the olive oil over medium heat.
Add the onion and garlic and cook until softened.
Add the broccoli florets and cook for 5 minutes, until tender-crisp.
Push the vegetables to one side of the skillet and add the shredded chicken to the other side.
Cook for 2-3 minutes, until heated through.
In a bowl, whisk together the eggs, milk, salt, and pepper.
Pour the egg mixture over the chicken and vegetables in the skillet.
Cook, stirring occasionally, until the eggs are fully cooked.
Serve hot and enjoy!