In a large pot, combine halved baby potatoes with enough salted water to cover them completely. Bring to a boil over high heat and cook for 10–12 minutes until fork-tender. Drain and set aside.

In a large skillet, melt 3 tablespoons of unsalted butter over medium heat. Add minced garlic and sauté for 1–2 minutes until fragrant. Be cautious not to brown the garlic.

Lower the heat to medium-low and stir in 1 cup of heavy cream, ½ cup of broth, ½ teaspoon of salt, ¼ teaspoon of pepper, and 1 teaspoon of mustard. Simmer gently for about 5 minutes, stirring occasionally.

Carefully fold the boiled potatoes into the creamy sauce in the skillet. Stir gently and allow to simmer together for 2–3 minutes.

Taste the sauce and adjust seasoning as necessary. Sprinkle with chopped parsley before serving.