Peel the potatoes or leave the skins on, depending on your taste. Cut them into even chunks about one inch thick. Drop them into a large stockpot of cold water as you go.
Add enough cold water to sit about one inch above the potatoes. Stir in one tablespoon of salt, then bring everything to a boil over high heat. Lower to medium-high and cook for 10 to 12 minutes, until a knife slides in with almost no resistance.
While the potatoes boil, melt one tablespoon of butter in a large sauté pan over medium-high heat. Add the minced garlic and cook for about two minutes, stirring now and then. Once it is lightly browned, move it to a plate.
Melt the remaining butter in the same pan over medium-high heat. Stir often until it foams and the milk solids turn golden and smell toasty. Pour it straight into a heat-safe bowl, because it can burn in seconds.
Drain all the water from the potatoes. Put them back into the hot pot over low heat. Shake the pot gently for about one minute to cook off the steam.
Take the pot off the heat. Add the brown butter, garlic, warm milk, and Parmesan. Mash until the potatoes reach your favorite texture, adding a splash more warm milk if needed.
Taste the potatoes and add salt and black pepper. I usually need a generous pinch of salt to make the flavors pop. Stir just until combined so the potatoes stay light.
Spoon the potatoes into a warm bowl while they are still steaming. Top them with chopped chives or green onions and a little cracked black pepper. Serve right away for the creamiest bite