Put the potatoes in a large pot of cold, well salted water to cover. Bring to a boil and cook until a knife slips in easily, 15 to 20 minutes. Drain the potatoes. Place on a cookie sheet and refrigerate until cool.
When they are cool enough to handle, hold 1 between your hands as if you were clapping and press gently with the heel of 1 hand. You want to smash the potato to about a 1/2-inch thickness while keeping it in 1 piece. The skin will split, but the potato should not fall apart. Repeat with the remaining potatoes. You can prepare the potatoes to this point several hours ahead.
Pour 1/2-inch of peanut oil in the large skillet and heat over moderately high heat.
Combine the parsley, garlic, and lemon zest in a serving bowl and set aside.
When the oil begins to smoke, carefully put the smashed potatoes in the oil and cook on both sides until crisp and well browned, 8 to 10 minutes. With a slotted spoon, transfer to paper towels to drain. Season with salt and pepper.
Heat the olive oil in a small skillet over moderately high heat. Add the garlic and saute until lightly browned. With a slotted spoon, transfer the garlic to the bowl with the parsley-lemon mixture.
When the potatoes are ready, add them to the garlic mixture and toss gently. Serve immediately. Save the leftover garlic oil and use it to dress a salad or vegetables the following day.