Bring the frying pan up to a medium heat (about 50% to 60%) and add about two tablespoons of olive oil. Enough so that when you swish it around the pan it coats the bottom nicely. Then add in the onion and fry till soft and translucent. Add in the garlic at around this time to soften up as well. Stir in the sliced parsnip and carrots using your spatula. Once all the vegetables are nice and soft, pour them into the casserole dish
Take your diced venison and rinse it if you need to, before allowing it to dry slightly on a kitchen towel. Add some more olive oil to your now empty frying pan, and bring it up to a medium high heat (think about 70% to 80% of max). Then take each piece of venison and coat it lightly in the plain flour, before putting it in the frying pan. Once all the pieces are cooking away, move them around using your spatula to get them evenly cooked. You're only trying to cook the outer edges of the meat (sealing it), so don't fry them for more than 5 to 10 minutes. Once that's done, pour the venison, including any juice, into the casserole dish.
Add in the ginger and red currant jam into the casserole dish and pour in some boiling water in order to fill the dish to just below the top of the contents. Give it a stir with your spoon. Take the fresh herbs, finely chop a reasonable amount up, add them into the casserole dish and give it all another stir. Add some black pepper and a pinch of salt, then cover with the lid. Cook in the oven at about 180C for about an hour. After that, check it, give it a stir and check to see if the venison is cooked through. If it isn't, put it back in the oven for longer, checking every 10 mins or so.
Once you're happy it's cooked, remove the lid from the casserole dish. Roll out the puff pastry on to the dish, covering your cooked pie innards. If you need to roll it out from a block of pastry, aim for something about as thick as a £1 or 1 euro coin. Trim the excess pastry off with a knife, and make some pretty decoration on the top of the pie if you want to. Make sure to pierce it in 2 or 3 places to allow steam to escape. Glaze the pastry with milk using the glazing or pastry brush. Turn the oven up to 200C then put the pie back in for a further 20 mins, or until the pastry has risen and turned a golden brown. Serve.