Cook the potatoes. Add the peeled and cut russet potatoes to a large pot and cover with cold water by about 1 inch. Add 1 tablespoon Diamond Crystal kosher salt to the water and bring to a boil over high heat. Reduce the heat to maintain a gentle boil and cook for 15–20 minutes, or until the potatoes are completely tender and easily pierced with a fork.
Brown the butter. While the potatoes cook, melt the butter in a light-colored skillet or small saucepan over medium heat. Continue cooking for about 4–6 minutes, swirling the pan occasionally, until the butter foams, develops golden-brown bits, and smells nutty. Watch carefully, as it can go from browned to burnt quickly.
Add the garlic. Remove the browned butter from the heat and let the bubbling subside for 30–60 seconds. Stir in the minced garlic and allow it to cook gently in the residual heat for about 30 seconds, stirring constantly. Set aside.
Warm the cream. Heat the ¾ cup heavy cream in a small saucepan over low heat or in the microwave until warm but not boiling.
Drain and dry the potatoes. Drain the cooked potatoes thoroughly, then return them to the warm pot over low heat for 1–2 minutes, stirring gently to evaporate any remaining moisture. Remove from the heat.
Mash the potatoes. Mash the potatoes using a potato masher, or pass them through a potato ricer for an extra-smooth consistency. Avoid overworking the potatoes, which can make them gummy.
Add the browned butter and Boursin. Pour the browned butter and garlic over the potatoes, making sure to scrape in all the flavorful browned bits. Add the softened Boursin cheese and gently fold everything together until the cheese is melted and evenly incorporated.
Finish with cream and seasonings. Gradually stir in the ¾ cup warm heavy cream until the potatoes are creamy and smooth. Add another 2–4 tablespoons of warm cream if needed to reach your desired consistency. Fold in the sliced scallion greens and black pepper. Taste and add additional kosher salt as needed.
Garnish and serve. Transfer the mashed potatoes to a serving bowl, garnish with additional sliced scallions, and serve warm.