Preheat the oven to 225°C.
Heat clarified butter in a large ovenproof frying pan and layer potatoes in a circle to cover the base.
Cover potatoes with anchovies, ensuring they are skin-side up with tails pointing towards the centre.
Scatter marjoram over the tart, layer tomatoes on top, season, and bake for 6-8 minutes.
Blanch basil in boiling salted water for one minute, then refresh in iced water.
Squeeze water from basil and blend with olive oil for two minutes until smooth, then strain through a sieve.
Toss rocket with olive oil, place on tart slices, and drizzle with the prepared basil oil.