Adjust the rack to the lower third and preheat the oven to 450 degrees Fahrenheit. Toss the potatoes with the salt, pepper, and 2 tablespoons of the olive oil in a large, shallow pan (1-inch deep). Roast, without turning or stirring, until the underside are golden brown, about 20 minutes.
Meanwhile, in a small bowl, whisk together the anchovies, lemon juice, and remaining tablespoon of olive oil.
Turn the potatoes over with a spatula and roast for 10 minutes more. Toss with the garlic and roast for 5 minutes more. Transfer to a bowl and stir in the anchovy mixture, parsley, and salt and pepper to taste.