Preheat the oven to 400°F.
Combine ¾ cup sour cream, ¼ cup mayo, herbs, lemon zest, lemon juice, and seasonings (½ teaspoon garlic powder, ½ teaspoon onion powder, and ½ teaspoon kosher salt) in a bowl. Adjust seasonings to taste. Place in the fridge to allow the flavors to come together while the potatoes roast.
In a mixing bowl, combine the potatoes and 2 tablespoons of olive oil, 1 tablespoon of melted butter, 1.5 teaspoons salt, 1 teaspoon garlic powder, 1 teaspoon onion powder, ½ teaspoon oregano, ¼ teaspoon smoked paprika, and ¼ teaspoon black pepper. Toss to combine.
Add the remaining 2 tablespoons of olive oil and 2 tablespoons of melted butter to the bottom of the baking dish. Make sure the bottom is coated evenly with the cooking oils.
In a separate bowl, combine the parmesan cheese with the remaining seasonings (½ teaspoon salt, 1 teaspoon onion powder, 1 teaspoon garlic powder, ½ teaspoon oregano, ¼ teaspoon smoked paprika, and ¼ teaspoon black pepper). Toss to combine. Add the parmesan mixture to the bottom of the baking dish in an even layer as possible, trying not to move it much once it's placed down.
Place the potatoes scored side down into the parmesan mixture. Make sure there's not much room between the potatoes. Bake for 40-45 minutes, until the potatoes are softened and the parmesan crust is golden brown. Allow for the potatoes to cool in the baking dish for about 7-10 minutes to let the cheese harden before enjoying. Serve right away with dipping sauce and enjoy!
Store potatoes and dipping sauce in separate airtight containers in the fridge for up to 4 days. Reheat the potatoes gently in the air fryer or in the oven (these are the best methods for crispiness) or in the microwave. Do not freeze.