Cut stem end off figs about 1/2-inch down. Use a melon baller or small spoon to hollow out the fig. Chop and reserve the insides of the figs. Set the figs aside. The stem pieces may be saved as "hats" for the presentation.
Heat the olive oil in a medium saute pan. When the oil is hot but not smoking add the fennel. Toss or stir the fennel until golden. Season with salt and a touch of black pepper. Remove the pan from the heat and add the lemon zest, reserved fig insides and tarragon. Finish with the extra virgin olive oil, adding just enough to have the filling bind together.
Remove the filling from the pan and let cool.
Rinse, then finely chop the green peppercorns.
In a small bowl, whisk together the balsamic vinegar, extra virgin olive oil and shallots. Season with salt after adding the peppercorns, as they can be salty. The vinaigrette can be made a day in advance and held refrigerated.
Let the vinaigrette sit for about a half hour at room temperature before serving if you have refrigerated it.
Just before serving, fill each fig with cooled fennel mixture. Cover with reserved stem pieces if you wish.
Place 2 figs on a plate along with a wedge of the cheese. Drizzle the figs with the vinaigrette.
Some suggested garnishes are fresh grape leaves, the fine inner leaves of the fennel bulb, or chervil plunches.