Place the red potatoes in a large pot and cover with cold water. Add 1 tablespoon salt and bring to a boil. Reduce heat to medium and simmer for 15-20 minutes or until the potatoes are fork-tender but still hold their shape.
Drain the potatoes thoroughly and let cool for about 20 minutes before cutting into bite-sized cubes.
While the potatoes are cooling, whisk together olive oil, fresh lemon juice, dried oregano, garlic (if using), lemon zest (if using), ½ teaspoon salt, and ¼ teaspoon freshly ground black pepper in a small bowl to create the dressing.
In a large mixing bowl, combine the cooled potato cubes, finely diced red onion, diced cucumber, sliced Kalamata olives, and diced red bell pepper (if using).
Pour the prepared dressing over the potato mixture and toss gently to ensure all ingredients are evenly coated.
Carefully fold in the crumbled feta cheese and fresh dill (if using), being gentle to prevent the cheese from breaking down completely.
Cover the bowl and refrigerate for at least 30 minutes (though 1-2 hours is ideal) to allow the flavors to meld together.
Before serving, taste and adjust seasoning if necessary, adding more salt, pepper, or lemon juice as desired.