Add the potatoes to a large pot and cover with water by 1 inch. Add the salt. Bring to a boil, then reduce the heat to maintain a steady simmer. Cook for 15 minutes, or until the potatoes are very soft.

While the potatoes cook, set a small saucepan over low heat and add the vegetable broth. Gently simmer just until warm, then set aside.

Drain the potatoes well, then return them to the warm pot. Let them stand for 1 minute so the extra moisture can evaporate.

Pour in ½ cup of the warm broth and mash to your preferred consistency. If the potatoes feel too thick, add a little more broth, as needed.

While the potatoes are still hot, add the Boursin cheese. Stir until fully melted and incorporated.

Season to taste with salt and black pepper.

Stir in half of the parsley and chives.

Transfer to a serving bowl and top with the remaining herbs. Drizzle with melted butter, and serve warm.