Add the dry ingredients to a bowl and rub the butter and the lard in until you have a mixture that resembles breadcrumbs.
Add in the water, adding just enough until all of the flour is absorbed. Split into two discs and place in the fridge for 1 hour.
For the burger:
Fry the onion and garlic until soft. Add to a bowl along with the mince, parmesan, egg and breadcrumbs. Mix together to form one large patty. Make a well with your finger in the centre of the patty and stuff with mozzarella and cheddar. Reshape into a patty.
Heat a few tbsp of olive oil in a pan and fry the patty until golden on either side. Place to one side to cool.
Roll the first disc of pastry out and lay the burger patty on top. Using a small plate, slightly larger than the size of your patty, cut off the excess dough.
Place the cooled patty on the disc, along with some cheddar cheese on top and some egg wash around the outside.
Roll the second pie dough out into a slightly larger disc than the previous one, and drape this over the top of the burger patty. Stick the edges of the pastry together with your hands, removing air pockets, and crimp the edges with your finger and thumb to create a pattern.
Egg wash the top and add a sprinkle of sesame seeds. Bake at 180C for 30-40 minutes, or until golden brown on top.