Preheat the oven to 450°F (230°C).
Place the potatoes in a large pot and cover with cold water. Bring to a boil, then reduce heat and simmer until just fork-tender, about 10–15 minutes depending on size. Drain and let cool slightly.
Brush a baking sheet with 1 tablespoon of the olive oil. Arrange the potatoes on the sheet and gently smash each potato once with your hand or the bottom of a glass to flatten slightly while keeping them mostly intact.
Drizzle the remaining olive oil over the smashed potatoes and sprinkle with a pinch of kosher salt and black pepper. Roast in the oven until golden and crispy, about 25–30 minutes.
While the potatoes roast, whisk together the Greek yogurt, buttermilk, minced garlic, Dijon mustard, chopped chives, chopped dill, and a pinch of salt and pepper in a bowl to make the dressing.
When the potatoes are done, remove them from the oven and let cool slightly. Transfer to a large bowl and pour the dressing over the warm potatoes, tossing gently to coat. Add extra chopped herbs if desired and adjust seasoning with more salt and pepper to taste.
Serve immediately warm or chilled, garnished with additional chives and dill if desired.