Preheat an oven to 180C degrees. Place a large saute pan on a high heat and add the vegetable oil.
Season the diced venison with salt and then brown in the pan, in batches if necessary. When the venison is browned all over remove from the pan and set aside on a plate.
Reduce the heat to low then pour the flour into the pan and mix well. Cook out the flour for 2 minutes then gradually add the venison stock. Keep stirring to create a smooth thick sauce.
Into the large ovenproof pan layer half of the venison then top with half of the potatoes, onions, leek and carrot. Repeat the process with the second half of the ingredients to form a second layer.
Pour the thickened venison stock and thyme leaves into the saucepan then cover with a lid.
Transfer the Irish stew to the oven and cook for 1 hour.
The meat and vegetables should be tender after 1 hour, season with salt to taste. Remove from the oven and serve sprinkled with freshly chopped parsley.