Place the peeled and cubed potatoes in a large pot and cover with cold water. Add 1 tablespoon of salt to the water and bring to a boil over medium-high heat.
Once boiling, reduce heat to medium and simmer until the potatoes are fork-tender but still hold their shape, about 8-10 minutes.
While the potatoes are cooking, prepare an ice bath by filling a large bowl with ice and cold water.
Drain the cooked potatoes in a colander and immediately transfer them to the ice bath. Let them cool for about 5 minutes.
Drain the cooled potatoes thoroughly and transfer to a large mixing bowl. Let them air dry for a few minutes.
In a small bowl, whisk together the olive oil, red wine vinegar, minced garlic, Dijon mustard (if using), dried oregano, red pepper flakes (if using), salt, and black pepper to create your dressing.
While the potatoes are still warm (but not hot), pour half of the dressing over them and gently toss to coat.
Add the thinly sliced red onion, diced red bell pepper, halved black olives, and capers (if using) to the potatoes and gently mix.
Let the mixture cool to room temperature, then refrigerate for at least 30 minutes to allow the flavors to develop.
Just before serving, add the mozzarella cubes, sun-dried tomatoes (if using), torn fresh basil leaves, and chopped parsley (if using).
Drizzle the remaining dressing over the salad and toss gently to combine all ingredients.
Taste and adjust seasoning with additional salt and pepper if necessary before serving.
