Peel the potato, cut it into 2 cm cubes, and boil it in salted water for 12 to 15 minutes until tender. The pieces should yield easily to a knife without breaking down into mush.
Drain the potato well, leave it to steam dry for a minute or two, then mash it in a medium mixing bowl. The mash should look dry and a little crumbly rather than creamy or glossy.
Drain the tins of mackerel thoroughly, flake the fish, and fold it into the warm mashed potato. The fish should break up evenly through the mash without making it wet.
Roughly chop the capers, finely chop the parsley, add both to the bowl, and season to taste. The mixture should smell fresh and savory, with the capers giving it a sharp briny edge.
Shape the mixture into 4 fish cakes and chill them in the fridge for 10 minutes. They should feel firmer and easier to handle after this first chill.
Put the flour in one shallow bowl, the beaten egg in a second, and the breadcrumbs in a third, then crush the fennel seeds into the flour. The dredging line should be ready before you coat the cakes so the crust stays neat and even.
Dip each cake in the flour, then the egg, then the breadcrumbs, and return them to the fridge for another 10 minutes. The coating should fully cover the surface and look dry, not patchy.
Heat the cooking oil and butter in a frying pan over medium-high heat. When the butter foams across the pan, the fat is hot enough for the cakes to go in.
Fry the cakes for 2 to 3 minutes per side, basting with the butter as they cook. The crust should turn deep golden and crisp while the center stays tender and hot.