Trim fennel and cut off the 2 outer ends of the fennel then slice directly in half the long way. Sweat the garlic cloves in olive oil to infuse garlic flavor. Deglaze with muscat, verjuice and chicken stock. Add the fennel, thyme, salt, sugar, and peppercorns. Cover with parchment paper and braise until tender. Drain, cool and reserve juice (use to poach fish, if desired).
While the fennel is cooling, place 1/2 tablespoon of butter in each of the cast iron pans. Put 1 tablespoon of sugar on top of the butter and sprinkle in a pinch of salt. Place 1 piece of fennel in each pan and cook over direct heat until caramel forms.
Place a piece of semi-cooked tart pastry on top of each fennel and finish in a preheated 350 degree oven for about 5 minutes. Turn upside down and serve warm.
Sift flour, sugar and salt together, cut in the butter. Using the well method, add the egg. Allow at least 30 minutes to rest. Roll the dough out to about 1/8-inch thick and cut with a round cookie cutter, which would be the same size as the cast iron pans. Place the dough in between 2 sheets of parchment on a tray and chill. Put a second tray on top of the tarts and bake in a preheated 350 degree F oven for about 5 minutes.