Place the potatoes in a pot, covering them with 2 quarts of cold water. Add the salt, then bring the water to a boil over high heat.
Once boiling, reduce the heat to a simmer and let the potatoes cook uncovered for about 13 to 15 minutes, or until they are tender when pierced with a knife. Start checking around 12 minutes to avoid overcooking.
Meanwhile, as the potatoes cook, prepare the cream sauce. Melt the butter in a large sauté pan over medium heat. Add the garlic and stir for about 30 seconds until fragrant.
Gradually whisk in the flour, cooking for another minute until the mixture turns lightly golden. Slowly pour in the chicken broth, whisking continuously until the sauce begins to thicken.
Add the half-and-half, Parmesan cheese, and cayenne pepper, stirring frequently. Season with salt and pepper to taste, adjusting the thickness by adding more milk if needed.
Once the sauce is ready, toss the drained potatoes into the pan, making sure they’re fully coated. Finish by sprinkling fresh parsley on top before serving.