Wash the salmon well both inside and out, then pat dry with kitchen paper (leaving the scales on helps to keep in the moisture as it cooks).
Finely slice 1 lemon and the fennel into rounds and stuff into the salmon cavity with the parsley, marjoram and chives.
Combine the rock salt, eggs and 250ml of water in a large bowl, then evenly spread one-third of the salt over a large baking tray (roughly 35cm x 45cm), making a slight hollow in the middle to hold the salmon snugly.
Lay the salmon diagonally into the tray, then spoon over the remaining salt mixture, heaping it around and onto the salmon so that it’s evenly covered – you should have a layer of salt, roughly 2cm thick, all over the salmon.
Place the tray in the hot oven for around 35 minutes, or until cooked through. To test if the salmon is ready, push a skewer through the salt into the thickest part of the fish – if it comes out warm after 5 seconds, it’s done.
Meanwhile, make the basil yoghurt. Pick the basil leaves into a blender, add the mustard, the juice of half a lemon and half the yoghurt. Blitz until smooth, then fold back through the rest of the yoghurt with 4 tablespoons of extra virgin olive oil, and season to taste.
To make the salsa, deseed and finely chop the chilli with the mint leaves and a drizzle of honey, then place into a bowl with 2 tablespoons of extra virgin olive oil and the vinegar, and season to perfection.
Once cooked, remove the salmon from the oven and allow to cool for no longer that 1 hour, then with the tip of a knife, carefully slice into the salt, cutting all the way along the salmon spine, being careful not to slice into the fish at this point. Gently lift the salt casing off the salmon, then spoon away and discard the remaining salt, brushing away any excess from the top of the salmon.
Transfer the fish to a large platter, then score the skin along the spine, across the tail and under the gill and peel back the skin.
Divide up the salmon and serve with the basil yoghurt, chilli salsa and lemon wedges for squeezing over.