In a small saucepan gently fry the anchovies in their olive oil for 2 minutes or so until they have totally collapsed – you will see this happen when you stir them with a spoon. Add the garlic, lemon zest and black pepper before pouring in the wine. Bring up to a simmer then turn off the heat and leave to cool.
Put the venison fillet into a bowl and pour over the marinade. Leave to marinate for 4 hours.
In the meantime, make the green sauce. Mix together the tarragon, marjoram, capers, shallot, lemon juice, olive oil and garlic then season with sea salt to taste.
Heat a griddle until hot. Remove the venison from the marinade and sear on the hot griddle for 3-4 minutes on each side, brushing occasionally with the marinade – it should be well coloured on the outside and pink in the middle.
Toast the sourdough bread and spread the mustard over 4 slices. Slice the venison and lay it on top. Spoon over the green sauce then top each with a remaining slice of toast. Eat immediately.