Rub the butter into the flour until the mixture resembles fine breadcrumbs. Mix in the egg, salt and lemon juice and knead until a dough forms. Wrap in cling film and chill in the fridge for 30 minutes.
Preheat the oven to 190 C / Gas 5. Grease a quiche dish.
For the filling:
In a large bowl whisk eggs, milk and cream together. Stir in the feta cheese then add the broccoli, ham, onion, garlic and spices. Mix well.
Roll out the pastry on a floured surface and line the bottom and sides of the prepared quiche dish.
Place in the preheated oven and bake for 10 minutes until lightly golden brown (lining with baking parchment and filling with dried beans will help with this. Discard after using).
Remove from the oven and pour the filling into the pastry case.
Bake for additional 45 minutes until the filling is firm. Remove from the oven and serve hot or cold.