Start the potatoes. Place 1½ pounds whole potatoes in a pot and cover them with cold water.
Boil until tender. Bring the water to a boil and add 1 tablespoon salt. Lower the heat and simmer for about 15–25 minutes, depending on the size of the potatoes. They’re ready when a fork slides in easily.
Cool and cut. Drain the potatoes and leave them to cool for a few minutes. Cut them into bite-size chunks. Peel them if you prefer, or leave the skins on.
Whisk the dressing. In a small bowl, combine 4 tablespoons extra virgin olive oil, 3 tablespoons red wine vinegar, 2 teaspoons mustard, 1 teaspoon dried oregano, ½ teaspoon salt, ¼ teaspoon black pepper, 1 teaspoon lemon zest, and ½ clove finely grated garlic if using. Whisk until combined.
Dress the warm potatoes. Put the warm potato chunks into a large bowl. Pour the dressing over them and gently toss. Don’t worry if some pieces break apart, since the softer edges help make the salad creamier.
Add the remaining ingredients. Add 1½ cups cherry tomatoes, 1 small red onion, ½ cup olives, 2 tablespoons capers, ½ cup chopped parsley, and ½ cup crumbled feta.
Toss gently. Mix everything carefully until combined. Taste and adjust the salt, pepper, or vinegar if needed.
Finish the salad. Transfer it to a serving platter. Sprinkle with a little extra oregano and finish with a light drizzle of olive oil.