Wash the baby potatoes thoroughly under cold running water and chop larger ones in half. Set aside.

In a large pot, bring salted water to a rolling boil. Add the baby potatoes and cook for about 12–15 minutes until fork-tender. Drain and set aside.

In a skillet, heat olive oil or butter over medium heat. Add minced garlic and chopped onion (if using), sauté for 1–2 minutes until fragrant.

Pour in the heavy cream and broth, stirring to combine. Season with salt, pepper, and thyme or Italian seasoning. Allow to simmer for 3–4 minutes.

Add the drained baby potatoes to the skillet and toss to coat with the sauce. Simmer for an additional 2–3 minutes, adding Parmesan cheese if desired.

Transfer to a serving dish and finish with chopped parsley. Serve warm.