Boil the octopus for 1 hour per kilo of octopus in plenty of water with some salt, bay leaf, allspice grains and a dash of vinegar or wine.
Bring ¼ liters of white wine vinegar with a teaspoon of white caster sugar to the boil and then pour into a preserving jar. Peel a shallot and use your mandoline on the thinnest setting to cut very thin rings. Add the onion rings to the vinegar and let sit for at least an hour.
Remove the rack from your oven and preheat the oven to 100 degrees. Place a piece of baking paper on the rack. Cut your mini tomatoes in half lengthwise, sprinkle some salt and pepper over them and put them in the oven for an hour.
An hour before you want to serve, cut the fennel in half lengthwise and remove the hard heart and stems. Cut them into thin slices with the mandolin on the thinnest setting.
In a glass or bowl, mix 1 teaspoon of white caster sugar, 1 teaspoon of mustard, a dash of good olive oil and a dash of white wine vinegar and pour the dressing over the fennel. Mix this well and then cover it (with cling film).
Strip the leaves from a few sprigs of tarragon and chop the leaves finely. Mix them with 3 tablespoons of mayonnaise.
After the indicated cooking time, let the octopus cool and cut the eight legs loose from the central part (where the mouth is located). Remove the jaws and cut the body/bag loose. Cut the central body part into pieces.
Mix half a teaspoon of smoked paprika powder with some olive oil and rub the 8 legs and the center parts with it.
Grill the octopus parts until crispy and colored in a grill pan or on the barbecue. This is purely for taste because they are already cooked and soft.
Then divide the fennel salad among 4 plates, place 3 pickled shallots, 6 tomato halves, 3 dollops of tarragon mayonnaise and 2 octopus arms on each plate and garnish with a cress.