Place the halved baby potatoes into a saucepan filled with salted water. Set over high heat and bring to a boil. Cook until the potatoes are tender when pierced with a fork, approximately 10 to 12 minutes. Drain thoroughly and set aside.
In a large skillet, warm the butter together with the olive oil over medium heat. Once melted, add the finely minced garlic. Sauté for about 1 to 2 minutes, taking care not to let the garlic brown.
Pour in the broth and cream, stirring to combine. Let the mixture gently simmer for 3 to 4 minutes, allowing it to slightly reduce and thicken.
Incorporate the grated Parmesan, Italian herbs, salt, and pepper into the sauce. Stir until the cheese is fully melted and the sauce turns smooth and rich.
Transfer the cooked potatoes into the skillet with the sauce. Carefully stir to coat each piece evenly with the creamy garlic mixture.
Remove from the heat. Finish by sprinkling with freshly chopped parsley. Serve warm as an accompaniment to your favorite main course.