Place the potatoes into a large saucepan, cover with well salted water and bring to the boil. Cook for 10 to 12 minutes, depending on their size, until they take the point of a knife with ease. Drain in a colander and leave them to steam dry for a few minutes.
Return the pan to the heat, add the butter and 1 tablespoon of the olive oil and, when it begins to foam, stir in the garlic. Cook gently for 1 minute, then return the potatoes to the pan. Add the lemon zest and half the lemon juice, season well with salt and pepper and fold through the chopped chives and fennel tops. Set aside and keep warm.
Toast the flaked almonds in a dry frying pan over a medium heat for 1 to 2 minutes until lightly golden. Tip them onto a plate.
Open out the squid tubes by slicing them down one side. Score the inside lightly in a criss-cross pattern, taking care not to cut all the way through, then cut into strips about 4 to 5cm wide.
Place the squid into a bowl with the remaining olive oil, the smoked paprika, fennel seeds, thyme leaves and a little salt and pepper. Toss everything together well.
Heat a barbecue or heavy ridged grill pan until very hot. Lay the squid onto the grill and cook for about 1 minute on each side, but no longer, so it stays tender.
Arrange the potatoes over a large serving platter. Scatter over the hot squid and the toasted almonds. Squeeze over the remaining lemon juice, drizzle with a little extra virgin olive oil and finish with a few more fennel tops or chive flowers if you have them. Serve straight away.
