1. Heat your oven to 180°C/Fan 160°C/Gas 4. Line a baking tray with foil and pop the salmon fillets on it, skin-side down. Scatter 2 tsp caraway seeds over to create a crust. Arrange the tomatoes around the salmon and drizzle them with 1 tbsp olive oil. Season with salt and pepper, then set to one side.
2. Scrub the potatoes. Coarsely grate them and place in a sieve over a bowl. Add a big pinch of salt and scrunch with your hands for 1-2 mins. Pop a plate over the potato and weigh it down with something like a tin of beans. Set aside for a few mins.
3. Separate the egg, placing the white in a large bowl and the yolk in a medium heatproof bowl. Add 1 tbsp mustard to the egg yolk with 1 tbsp of lemon juice. Season. Put to one side.
4. Peel and finely chop the onion. Finely chop the parsley stalks, setting the leaves aside for later. Whisk the egg white till it's frothy (use a fork if you don't have a whisk). Add the onion, parsley stalks and flour to the egg white and mix together to form a paste. Season generously.
5. Give the potatoes a final squeeze and pop them in the bowl with the egg white and onion. Pour the water from the bowl the potatoes drained over and in the bottom there should be a layer of starch. Scrape this into the potatoes. Give it a good mix.
6. Set a large frying pan on a medium-high heat. Divide the potato mix into 4. Shape one of the quarters into a ball, squeezing out any liquid. Flatten it in the palm of your hand. Pour 2 tbsp oil into the warm pan. Add the latke. Repeat with the remaining 3 portions (if you have a small frying pan, you may need to cook these in batches).
7. Cook the latkes for 3-4 mins till dark golden brown underneath, then flip over. Cook for a further 3-4 mins. Turn the heat downto the lowest setting and gently cook for 12-15 mins more, turning over every so often so they don't burn but do cook through.
8. While the latkes cook, slide the salmon and tomatoes into the oven for 12 mins. Completely melt the butter in a small pan then remove from the heat. Very slowly trickle it into the egg yolk mix (to avoid the sauce splitting), whisking vigorously to combine. You should have a thick yellow sauce.
9. Remove the salmon from the oven. Place a couple of latkes on 2 warm plates. Top with the salmon and a few roasted tomatoes. Pour over the hollandaise. Scatter over the parsley leaves and serve with lemon wedges for squeezing.