Prepare the potatoes: Peel the potatoes and cut them into evenly sized chunks. This helps them cook at the same rate.
Boil the potatoes: Place the potatoes in a large pot and cover them with cold water. Add a generous amount of salt to the water. If using garlic, add the peeled garlic cloves as well.
Cook until tender: Bring the water to a boil, then reduce the heat and simmer for about 15–20 minutes, or until the potatoes are completely fork-tender.
Brown the butter: While the potatoes cook, place the butter in a saucepan over medium heat. Let it melt and continue cooking until it becomes golden brown and develops a nutty aroma. Swirl the pan occasionally and watch carefully so the butter doesn't burn.
Drain the potatoes: Once tender, drain the potatoes thoroughly. Return them to the warm pot and allow them to sit for a minute or two so excess moisture can evaporate.
Warm the cream: Gently warm the heavy cream in a small saucepan or microwave. Do not let it boil.
Mash the potatoes: Mash the potatoes and garlic with a potato masher, ricer, or food mill until they reach your preferred texture.
Add the cream: Gradually pour in the warm cream, stirring gently until the potatoes become creamy. Add a little more cream if necessary.
Add the brown butter: Pour the browned butter over the potatoes and gently fold it in until evenly incorporated.
Add Parmesan: Stir in the freshly grated Parmesan cheese. Season with salt and freshly ground black pepper to taste.
Finish and serve: Transfer the mashed potatoes to a serving bowl. Garnish with fresh chives or parsley and, if desired, a little extra Parmesan and brown butter.