Preheat the oven to 400°F (200°C).
Wash the potatoes and make thin slices across the top about ⅛ inch apart, stopping just before cutting all the way through. Use chopsticks on each side as a guide if needed.
In a small bowl, mix melted butter, olive oil, grated garlic, salt, and pepper to create the garlic butter. Brush the garlic butter generously over the potatoes, letting it seep into the slits.
Place the potatoes on a baking tray and bake for 45–50 minutes, occasionally spooning pan drippings over them, until the edges are crispy and golden.
While the potatoes bake, combine Greek yogurt (or sour cream), mayonnaise, and grated garlic in a small bowl until smooth to make the creamy garlic sauce.
When the potatoes are done, sprinkle them with grated Parmesan and chopped fresh herbs.
Serve the potatoes hot alongside the creamy garlic dip.