In a heavy-bottomed pot, add the potatoes with enough cold water to cover them.
Add the salt, and place over high heat. When the water reaches a boil, reduce the heat to a simmer.
Continue to cook the potatoes until they are fork-tender (about 35-45 minutes). Drain the potatoes well and return them back to the heat to dry out slightly for about 30 seconds to a minute. For best results pass the potatoes through a potato ricer or food mill. If you do not have either of those pieces of equipment the potatoes can be mashed with a sturdy whisk, potato masher, fork, stand mixer, hand mixer, etc.
Heat the half and half until it is hot, add the butter and stir the mixture into the potatoes a little at a time until you reach your desired consistency. Fold in the brie until well incorporated.
Adjust the seasoning with salt and pepper, then transfer to a serving dish.
Garnish the potatoes with freshly chopped parsley and serve immediately. Enjoy!