Place the halved baby potatoes in a large pot and cover with cold water. Add 1/2 teaspoon of salt to the water. Bring to a boil over high heat.

Once boiling, reduce heat to medium and cook until the potatoes are fork-tender, about 12-15 minutes. Drain the potatoes in a colander and set aside.

In a large skillet or pan, melt the butter over medium heat. Add the minced garlic and sauté until fragrant, about 1 minute.

Pour in the heavy cream and chicken broth. Add the dried thyme, salt, and black pepper. Stir to combine and bring to a gentle simmer.

Reduce heat to medium-low and simmer the sauce for about 5 minutes, stirring occasionally, until it begins to thicken slightly.

Add the drained potatoes to the pan with the sauce. Gently toss to coat all the potatoes evenly with the creamy garlic sauce.

Sprinkle the grated Parmesan cheese over the potatoes and stir until the cheese has melted into the sauce.

Transfer the potatoes to a serving dish. Garnish with freshly chopped parsley and a sprinkle of additional black pepper. Serve hot.