Heat your oven to 200°C/Fan 180°C/Gas 6. Brush a baking tray with 1 tbsp olive oil and set aside.
Slice the celeriac in half, then slice the roots off 1 half at angle so you don't slice too much flesh off. Peel the celeriac half and coarsely grate it (if you have a food processor, roughly chop the celeriac into chunks and then whizz through the processor's grating attachment). Tip the grated celeriac into a mixing bowl. See our tip below on what to do with your leftover celeriac half.
Peel and coarsely grate the potato and add to the celeriac. Peel and finely slice the shallots and add them to the veg. Tip in 2 tbsp flour. Season with a pinch of salt and pepper. Stir to mix.
Crack the egg into a small bowl and whisk with a fork to break it up, then pour it into the veg and stir together till you get a sticky mixture.
Scoop 1 heaped tbsp out of the rösti mixture and drop it onto the baking tray. Flatten it out a little with the back of a spatula, then repeat with the rest of the rösti mix till you've used it all up.
Slide the röstis into the oven and bake for 30 mins till golden, crisp and cooked through – they should be tender when you slice into them.
While the röstis bake, make the crab salsa. Peel and finely chop the red onion and slide it into a small bowl. Dice the tomatoes and add them to the red onion. Finely chop the coriander stalks (keep the leaves for later) and add them to the bowl. Finely grate in the lime zest. Squeeze in the lime juice.
Flake the crab meat into the bowl, season with a pinch of salt and gently stir to mix.
When the röstis are cooked, pop them onto warm plates. Spoon the crab salsa over the top and garnish with the coriander leaves to serve.