Place the halved baby potatoes in a medium pot and cover with cold water by about 1 inch, then add a pinch of salt.

Bring the pot to a boil over medium-high heat, then reduce to a gentle boil and cook for 10 to 12 minutes, until the potatoes are just fork-tender but not falling apart.

Drain the potatoes well in a colander and set aside; pat dry with a clean towel if they appear very wet.

In a large skillet, melt the unsalted butter over medium heat.

Add the minced garlic to the skillet and sauté for 1 to 2 minutes, stirring often, until fragrant and lightly golden but not browned.

Stir in the heavy cream, broth, salt, black pepper, and Dijon mustard if using, and bring the mixture to a gentle simmer.

Simmer the sauce for about 5 minutes, stirring occasionally, until slightly thickened and able to coat the back of a spoon.

Add the drained baby potatoes to the skillet and gently fold them into the sauce until all pieces are evenly coated.

Simmer the potatoes in the sauce for an additional 2 to 3 minutes, allowing the flavors to meld and the sauce to cling to the potatoes.

Remove the skillet from the heat and sprinkle with grated Parmesan if using, stirring lightly to melt it into the sauce.

Garnish with chopped fresh parsley and adjust seasoning with additional salt and pepper if needed before serving warm.