In a large pot, add the potatoes and enough water to cover. Bring to a boil, salt it and cook until the potatoes are tender, about 15 minutes. Drain.
Meanwhile, in a large skillet, add the EVOO, 4 turns of the pan, and the garlic. Set over medium heat and fry the garlic until golden and crisp. Using a slotted spoon, transfer to a plate. Reserve the skillet with the oil.
On a cutting board, slice the steak thinly crosswise. Toss with a little flour and the paprika. Heat the reserved skillet over medium-high heat. Working in 2 batches, cook the meat until browned all over, 3 to 4 minutes. Transfer to a warm platter.
Stir the tomato paste into the skillet over medium-high heat for 30 seconds. Add the wine and scrape the bottom of the pan. Pour the sauce over the steak. Top with the watercress and reserved garlic chips.
Mash the potatoes with the sour cream, milk, horseradish and most of the chives; season with salt. Sprinkle the remaining chives on top. Serve alongside the steak.