Put potato chunks in a large saucepan over high heat and cover with cold water. Add salt and bring to a boil. Lower heat and simmer until potatoes are tender, about 20 minutes.
In a small saucepan over medium heat, combine heavy cream and all the herbs, except parsley, and bring to a simmer. Turn off heat and cover, allowing herbs to infuse for 15 minutes.
Drain potatoes well and pass through a food mill (or use a masher). Add butter and gradually stir in cream until potatoes have the desired consistency (you may not use all the cream). Stir in parsley, season with additional salt and pepper, and serve immediately. Enjoy!