Place the peeled and diced potatoes in a large pot and cover with cold water. Add 1 tablespoon of salt and bring to a boil. Cook until fork-tender but not mushy, about 12-15 minutes.
Drain the potatoes in a colander and spread them on a baking sheet to cool for 15-20 minutes.
In a large mixing bowl, combine the cooled potatoes, red onion, bell pepper, and green olives. Add the optional beets and/or hard-boiled eggs if using.
In a separate small bowl, whisk together the mayonnaise, lime juice, Dijon mustard, white vinegar, 1/2 teaspoon salt, and 1/4 teaspoon black pepper until smooth.
Pour the dressing over the potato mixture and gently fold to coat evenly, being careful not to break the potatoes.
Fold in the chopped cilantro, reserving a small amount for garnish.
Taste and adjust seasoning with additional salt, pepper, or lime juice if needed.
Cover and refrigerate for at least 30 minutes (ideally 2 hours) to allow flavors to meld.
Before serving, give the salad a gentle stir and garnish with the reserved fresh cilantro.
