1. Start by placing the halved baby potatoes in a large pot and covering them with salted water. Bring the water to a boil and cook the potatoes for 10 to 12 minutes, or until they are fork-tender. Drain the potatoes and set them aside.

2. In a large skillet, heat the butter and olive oil over medium heat. Add the minced garlic and sauté for 1 to 2 minutes, stirring constantly, until the garlic becomes fragrant and lightly golden.

3. Pour the heavy cream and chicken broth into the skillet with the garlic. Stir to combine and bring the mixture to a gentle simmer. Let the sauce simmer for 3 to 5 minutes, stirring occasionally, until it begins to thicken slightly.

4. Stir in the Parmesan cheese, salt, pepper, Italian herbs, and Dijon mustard (if using). Continue stirring until the cheese has melted completely and the sauce has become creamy and smooth.

5. Add the boiled baby potatoes to the skillet and gently toss them in the creamy garlic sauce, ensuring each potato is evenly coated. Allow the mixture to simmer for an additional 2 to 3 minutes, allowing the flavors to meld.

6. Remove the skillet from the heat and garnish the creamy garlic sauce baby potatoes with the fresh chopped parsley. Serve the dish warm as a delightful side accompaniment to your main course.