Preheat the oven 230C/450F/Gas 8. Brush a baking sheet generously with olive oil.
For the soda bread, sift the plain flour and the bicarbonate of soda into a big bowl. Add the salt, and mix with your hands. Make a well in the centre of the flour mix, pour in most of the buttermilk, and with one hand stiff and your fingers spread out like a claw, start mixing in a full circle once the butter milk has gone in.
Keep mixing like this until you have a soft dough. Do not knead it but work it very gently to bring it together.
Transfer to a floured surface, and roll it out to about 35x20cm/14x8in and transfer it to the oiled tray.
Brush the top of the dough with some more oil and sprinkle with a little sea salt. Transfer to the oven and cook for ten minutes. Then turn the oven down to 200C/400F/Gas 6 and cook for a further 8-12 minutes until cooked. When cooked, it should feel firm in the centre and be golden brown.
Transfer the soda bread from the oven to a wire rack and cool for a couple of minutes, then cut it into squares to serve.
Meanwhile for the soup, melt the butter in a heavy saucepan over a medium heat. When it foams, add the potatoes and onions and toss them in the butter until evenly coated. Season with salt and freshly ground pepper.
Cover with a circle of baking paper (to keep in the steam) and the saucepan lid, and sweat over a gentle heat for about ten minutes, until the vegetables are soft but not coloured.
Remove the paper lid. Add the celeriac and chicken stock, bring to the boil, reduce the heat and simmer for 8-10 minutes, until the celeriac is soft.
Liquidise the soup using a hand blender, adding a little more stock, milk (or cream) to thin to the required consistency. Season to taste with salt and freshly ground black pepper.
Serve the soup piping hot in a bowl with a scattering of chopped hazelnuts, and a little chopped parsley to garnish, accompanied by slices of soda bread.