Preheat the oven to 200ºC, fan 180ºC, gas mark 6.
Heat ½ tablespoon of the oil in a large frying pan. Cook the leeks for 10 minutes, adding the garlic for the last minute. Transfer to a bowl and set aside.
Add the remaining oil to the pan and fry the chicken over a medium heat for 5 minutes, until golden brown. Stir through the mustard and cheese, then add to the leek mixture.
In a saucepan, melt 25g butter and stir in the flour. Cook for 1 minute over a low heat, then remove from the heat and gradually add the chicken stock and milk, stirring well after each addition. Simmer for 2 minutes, until thickened. Stir in the lemon zest and juice, tarragon and peas.
Stir the white sauce into the chicken and leek mixture so that everything is evenly mixed. Pour into 6 x 450ml ramekins or individual pie dishes. Melt the remaining 25g butter and brush over the filo sheets. Scrunch the a piece of the buttery pastry over each pie, then bake for 25 minutes until the top is crispy and golden brown.
Meanwhile, boil the broccoli for 3-4 minutes, until tender. Drain and serve with the pies.