Start by thoroughly washing the baby potatoes under cold running water to remove any dirt. Set them aside and bring a pot of salted water to a boil.

Add the baby potatoes to the boiling water and cook for 12-15 minutes, or until fork-tender. Drain and let them steam to ensure they are dry.

In a skillet, melt butter or olive oil over medium heat. Add minced garlic and sauté for 1-2 minutes until fragrant and golden.

Pour in heavy cream and broth, then season with salt, pepper, and thyme. Stir and simmer for about 3-4 minutes until thickened.

Add potatoes to the skillet, tossing to coat in the sauce. Optionally, sprinkle with Parmesan and simmer for 2-3 minutes.

Transfer potatoes to a serving dish, garnish with parsley, and serve warm.