Cook the Potatoes:

Place the peeled and chopped potatoes in a large pot of cold salted water. Bring to a boil and cook until the potatoes are very tender, about 15-20 minutes.
Drain the potatoes well and return them to the pot. Let them sit for a few minutes to evaporate any excess moisture.

Prepare the Garlic:

While the potatoes are cooking, mince the garlic. You can also use a mortar and pestle to crush the garlic with a pinch of salt to create a smooth paste.

Make the Skordalia:

In a large mixing bowl, mash the hot potatoes until smooth. You can use a potato masher or a ricer for a smoother texture.
Gradually add the minced garlic, olive oil, and lemon juice (or vinegar) while continuously mixing. The mixture should become creamy and well-blended. Adjust the amount of garlic, lemon juice, and olive oil to taste.
Season with salt and pepper to taste.

Serve:

Transfer the skordalia to a serving bowl. Drizzle with a little extra olive oil and garnish with chopped parsley if desired.
Serve warm or at room temperature.