To make the potatoes: In a medium saucepan combine the vermouth, water, parsley, tarragon, lemon zest, and salt. Set aside.
Cut the potatoes in half horizontally. Slice a small portion off of the rounded ends-- so the potatoes stand up without rolling around -- and discard. Add the halved potatoes to the saucepan. Bring to a boil over medium heat; adjust the heat to maintain a gentle simmer and cook until just fork tender, about 8 minutes. Set the potatoes aside to cool in the liquid for 5 minutes.
Drain the potatoes, reserving 2 teaspoons of the cooking liquid. Discard the herbs and lemon zest. With a small spoon or melon baller, scoop out a little of each potato, to make a little "bowl" for the cheese.
Toss the potatoes with the oil in a small bowl, and stand them up on a baking sheet. Bake until lightly browned, about 15 minutes.
Meanwhile, make the filling: In a medium bowl, cream the cheese with the creme fraiche and the 2 teaspoons of reserved cooking liquid. Fold in the minced parsley, tarragon, chives, and chervil. Season with pepper, to taste.
Remove the potatoes from the oven and let cool slightly. While the potatoes are still warm, spoon a dollop of the cheese mixture into each potato. Set the potatoes on a platter and top off with the chive segments to garnish. Serve.