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1
Bring a 2-quart saucepan of water to a boil. Add the potatoes and cook until very tender when poked with a skewer or fork, 15 to 18 minutes, depending on their size. Drain and let cool.
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2
While the potatoes are cooking, pat dry the steak with paper towels. If it is much thicker than 1/2 inch, press it with your palms to flatten it slightly.
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3
Finely chop the garlic, sprinkle 1/2 teaspoon of salt onto it on your cutting board, and chop some more, smearing it with the side of your knife to make a paste. Rub the garlic paste into the steak on both sides. Generously season the steak with black pepper. Sprinkle the flour all over the steak, spreading the flour on lightly with your fingers. Gently shake off the excess flour.
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4
Pour the olive oil into a medium cast-iron skillet over medium heat. When the oil is shimmering, lay the steak in the pan and let it cook until the coating on the bottom turns golden brown, about 2 minutes. Turn the steak over and cook on the other side for another minute or so, for a medium-rare to medium steak. Transfer the steak to a plate and loosely cover it with aluminum foil to keep warm.
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5
Pour off all but a teaspoon or so of the oil from the skillet and return it to medium heat.
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6
When the potatoes are cool enough to handle, transfer them to your countertop and use a spatula or the side of a cook's knife and your palm to gently flatten them. Season lightly with salt, then use a spatula to transfer them to the skillet. Cook until golden brown, 2 to 3 minutes per side. (It's okay if they break up a little in the pan). Transfer the potatoes to the plate with the steak.
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7
Add the anchovy to the skillet, still over medium heat. Add the butter and cook until it melts and foams. Scrape up any browned bits in the pan, then stir in the lemon juice and parsley.
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8
Pour the sauce over the steak and potatoes, and eat.
