Heat the oven to 200C (180C fan)/390F/gas 6.
Bring a large pan of salted water to a boil, add the potatoes and cook for 10-20 minutes, depending on their size, until just cooked. Drain and leave in the colander to steam dry.
Tip the potatoes into a roasting tin, toss them with 50ml cornichon brine, two tablespoons of olive oil and salt and pepper to taste, then roast for 15 minutes.
Using a potato masher, squish the part-roasted potatoes until they crack and some of their soft, fluffy insides are exposed. Pour over another two tablespoons of olive oil and return to the oven for another 30-40 minutes, turning the potatoes once halfway, until golden and crisp.
Prick three fresh red chillies with the tip of a sharp knife – this stops them exploding when they are cooked. Using a pair of metal tongs, hold the chillies one at a time over a gas flame until they’re blackened and blistered all over (if you don’t have a gas hob, toast them in a hot, dry frying pan). Once they are all blistered, put the chillies in a small bowl, cover and leave for 15 minutes. They will steam in their own heat and the skins will peel off easily.
Once cool enough to handle, peel the chillies, open them up and scrape out and discard all the pith and seeds. Finely chop the flesh, put it in a large bowl with the remaining 70ml olive oil and the lemon juice, season to taste and mix well.
Once the potatoes are golden and crisp, add another 50ml cornichon brine while they are still hot, then toss with the roughly chopped cornichons and a generous grating of comte or vegan cheddar. Tear the radicchio into bite-size pieces, season with salt, toss in the chilli dressing and serve alongside the potatoes.
