Peel the potatoes, cut them into 1-2 inch chunks, and place them in a large saucepan. Add water to cover by an inch or two and 2 teaspoons salt. Bring to a boil over high heat. Lower the heat to a simmer and cook until the potatoes are very tender and just starting to fall apart, 10-20 minutes.
Meanwhile, combine the garlic, parsley, chives, tarragon, crème fraiche, and milk in the bowl of a blender. Blend on medium-high until very smooth, about a minute.
When the potatoes are cooked, drain them and put them back into the warm saucepan. Add the butter. Use a potato masher to mash the potatoes until fairly smooth. Mash gently and stop immediately if the potatoes start to feel sticky or gluey as overworking them can do. Alternatively, you can push the potatoes through a ricer to get them really smooth.
Pour the herb puree into the potatoes and stir gently to combine, adding more milk if the potatoes need it. They will continue to firm up as they sit, so you may wish to add more milk after a little while. Taste, adding pepper and more salt if you like.
If your potatoes are overly lumpy, push them through a colander with the back of a ladle and into a large bowl.
Serve the potatoes right away, topped with a drizzle of melted butter and a sprinkle of chives and pepper. See the make-ahead instructions below.
Notes
Make-Ahead: Make the potatoes as written and let cool to room temperature before scooping them into a container. Chill for up to 2 days. When ready to serve, scoop the potatoes into a large pot and add a big splash of milk. Cover and warm over low heat for 2-3 minutes. Uncover and stir gently. Repeat this until the mashed potatoes are hot. Alternatively, warm the mashed potatoes in a microwave.