To a large pot of salted water, add the potatoes. Fill with enough water to cover them. Bring to a boil over high heat.
Once boiling, reduce the heat to medium-high and continue cooking until the potatoes are fork-tender, about 25 minutes.
While the potatoes are boiling, brown the butter. In a stainless steel skillet or another light-bottomed pan over medium-high heat, melt the butter, swirling the pan occasionally. The butter will begin to foam, signaling that the water in the butter is boiling off. Watch closely at this stage, as browned butter and burnt butter are seconds apart. Tiny brown specks of milk solids will appear at the bottom of the pan; stir constantly and scrape the bottom with a spatula to prevent sticking.
As soon as the butter turns a chestnut brown color and smells nutty, remove the pan from the heat and set it aside.
Once the potatoes are cooked, drain them and return them to the pot. Remove the pot from the heat.
Using a potato masher, mash the potatoes. Add the browned butter, heavy cream, salt, and pepper. Continue mashing until everything is well incorporated and the potatoes are creamy.
Garnish with parsley and serve.