Prepare your Brussels sprouts: trim them and then halve them and set aside.
In a pan, melt the butter then add the chopped anchovy fillets and let them melt in it, roughly 2 to 3 minutes.
Add the sprouts and toss them, leaving them to cook for roughly one minute.
Turn down the heat to medium-low and add the lemon juice, sliced garlic, half of the chopped chives, brown sugar and chilli flakes. Cook everything for 2 minutes or so, until the liquid is reduced. turn off the heat and set aside.
In a small bowl whisk the eggs and parmesan, then season with salt and pepper and set aside.
Roll out your shortcrust pastry, fill it with the Brussels sprout mix leaving a gap of 3-4 centimetres on each side.
Fold the sides in, then pour the egg mixture and use some of it to brush the crust.
Preheat the oven to 180C and bake for 25-30 minutes, until the puff pastry is puffed up and golden in colour.
Serve warm.