Preheat oven to 400°F (200°C).
Heat olive oil and butter in a pan over medium heat. Add onion and garlic; cook until soft.
Stir in mushrooms and cook until tender. Add flour and stir for 1 minute.
Gradually add milk while stirring until thickened. Mix in mustard, salt, and pepper.
Add shredded chicken and remove from heat. Let the mixture cool slightly.
Roll out puff pastry and cut into squares. Fill each with chicken mixture and fold over.
Seal edges with a fork and brush with beaten egg.
Bake for 20–25 minutes or until golden and puffed. Serve warm.