Whisk yogurt, garlic, lemon juice, dill, salt and pepper together in a small bowl. Taste and add more salt or pepper if needed. Store in the fridge while you make the potatoes.
Preheat oven to 450°F. Line a baking sheet with foil and set aside.
Place potatoes in a large pot and cover with cold water. Season with salt and bring to a boil. Reduce to a gentle simmer and cook until potatoes are just fork tender but not falling apart, 10-15 minutes.
Meanwhile, combine melted butter, dried dill, oregano, marjoram, thyme, garlic powder, onion powder, cinnamon, nutmeg, ½ teaspoon kosher salt and black pepper in a large bowl. Drain potatoes and transfer to bowl with herb butter. Toss to coat.
Pour potatoes onto the prepared sheet pan and use the bottom of a mug to smash the potatoes until they’re ½-inch thick. Bake for 40-45 minutes, flipping halfway through, until golden and crispy.
Spread a large platter with yogurt dill sauce. Place crispy smashed potatoes on top. Garnish with fresh dill and serve hot.