Wash the potatoes thoroughly and place in a large pot. Cut any larger potatoes in half to ensure even cooking.
Cover potatoes with cold water, add a generous pinch of salt, and bring to a boil over medium-high heat.
Reduce to a simmer and cook until potatoes are fork-tender but not falling apart, about 15-20 minutes.
Drain the potatoes in a colander and allow to cool until just warm to the touch, about 10-15 minutes.
Transfer the warm potatoes to a large mixing bowl and gently smash them using a potato masher or fork, leaving chunks for texture.
Add the softened butter to the warm potatoes and stir gently until melted and incorporated.
In a separate small bowl, whisk together the sour cream, mayonnaise, and Dijon mustard until smooth.
Pour the creamy dressing over the buttered potatoes and fold gently to incorporate without overmixing.
Season with salt and freshly ground black pepper to taste.
Fold in the fresh chopped chives and any optional add-ins you desire.
Cover and refrigerate for at least 30 minutes (ideally 2 hours) to allow flavors to meld.
Before serving, taste and adjust seasonings if needed. If the salad seems too thick after chilling, add a splash of milk or extra mayonnaise to reach desired consistency.