Preheat oven to 200°C. Spray 4 medium sized ramekins or oven dishes with olive oil.
Place a medium heavy based pan over medium heat and add 1 tablespoon olive oil. Add the chicken and cook for 10-12 minutes or until cooked. Remove meat from the pot and set aside.
Add remaining olive oil to the pan and sauté leeks, garlic and mushrooms for 5-6 minutes, or until just softened. Add the flour and cook for 1-2 minutes. Add the milk and black pepper and cook for a further 4-5 minutes or until thickened. Return the chicken to the pot and stir to combine. Refrigerate mixture until cooled completely.
Meanwhile, bring a medium sized pot of water to the boil. Add potatoes and cook until tender, approximately 15 minutes, drain.
Bring a small pan of water to the boil. Add the broccolini and simmer for 4 minutes until tender. Drain.
Once chicken mixture has cooled, divide chicken mixture between ramekins/oven dishes. Roughly press down 1 piece of filo on top of every ramekin and brush with egg.
Bake for 20 minute or until golden. Serve with steamed greens and potatoes.