Place the scrubbed, halved potatoes in a pot of salted cold water and bring to a boil.

Cook the potatoes for 10 minutes until just tender when pierced with a fork, then drain well and let steam off for 1 to 2 minutes.

Heat the olive oil and butter in a large skillet over medium heat until the butter is foamy.

Arrange the potatoes cut side down in a single layer and cook for 4 to 6 minutes until the cut sides are golden and lightly crisp.

Add the minced garlic to the skillet and cook for 30 seconds, stirring frequently, until fragrant.

Pour in the heavy cream, add the salt and black pepper, and gently stir to coat the potatoes.

Simmer the potatoes in the cream over medium heat for 2 to 3 minutes until the sauce starts to thicken and cling to the potatoes.

Reduce the heat to low, sprinkle in the grated Parmesan, and stir until the cheese is completely melted and the sauce is smooth and creamy.

Taste and adjust seasoning with more salt or pepper if needed, then remove from the heat.

Sprinkle the potatoes with chopped parsley or chives and serve hot.