Place halved potatoes in a pot of cold, salted water, covering them by 1 inch. Bring to a boil and simmer until fork-tender, about 10–12 minutes.

Drain the potatoes thoroughly and let them steam dry in a colander for 5 minutes.

In a wide skillet, melt butter over medium heat until foamy. Add garlic and sauté for 1 minute, stirring constantly.

Immediately pour in cream and broth to prevent the garlic from browning. Add thyme, salt, and pepper. Simmer gently until the sauce thickens enough to coat the back of a spoon.

Gently fold in the steamed potatoes and simmer for 2–3 minutes.

Add Parmesan a handful at a time, stirring until melted and smooth. Adjust consistency with a splash more broth if needed.

Remove from heat, stir in chopped parsley, and let rest for 1–2 minutes.

Garnish with extra Parmesan and freshly cracked pepper before serving.