Peel and finely slice the shallots. Finely slice the celery. Place in a wide pan deep enough to take the salmon, add the fish stock, bring just to the boil and simmer for ten minutes. Season the salmon all over with salt and pepper. Add to the pan in a single layer with enough extra water to barely cover. Bring back to a gentle simmer, then cover with a lid, take off the heat and leave to poach gently until barely cooked - salmon is best when the flakes will separate easily but is still soft and pink in the middle. Remove when done.
Place the eggs in a pan of cold water, bring to the boil and simmer rapidly for 4-5 minutes - this should keep them just a little soft in the middle. Refresh under cold water, then remove the shell and cut in half.
Crush the garlic cloves and anchovies with a little pinch of coarse salt in a pestle and mortar, or with the flat side of a knife. Place in a bowl with the mustard, vinegar and egg yolks. Slowly whisk in the olive oil until thickened and emulsified, then whisk in enough water to give a thick salad dressing consistency. Season with black pepper and add finely grated parmesan.
Tear the bread into fairly small pieces. Bash the garlic cloves in their skins just so they split. Toss the bread with the garlic and olive oil, transfer to a baking tray and bake in a 180c oven until crispy. Drain on kitchen paper and remove the garlic.
Separate the lettuces into leaves, discarding any that aren't really fresh and crisp...but don't cut them. Toss with the dressing and arrange in bowls or on plates, making sure everyone gets a mix of large and small leaves.. Scatter over the croutons, gently flake over the salmon and add the egg. Finish with a little finely chopped parsley.
«For a classic Caesar salad, omit the salmon and egg and add three or four crisp rashers of streaky bacon per person instead. Or try any combination of salmon, bacon and egg - they will all work!»