To make the dough, combine flour, sugar, salt and butter in a bowl with your hands until it resembles a coarse meal. In a separate small bowl combine the ice water and vanilla and add it to the flour mixture and combine until the dough forms a ball. Wrap the dough in plastic and refrigerate it for 30 minutes.
On a lightly floured board roll out the dough to 1/4-inch thick and large enough to fit into a 9-inch tart pan. Trim the edges and prick the bottom of the dough with a fork. Line the crust with parchment paper and weigh it down with dry beans. Bake the dough in the oven for 20 minutes and then remove.
Lower the oven temperature to 375 degrees.
In an electric mixing bowl beat softened butter and sugar until the mixture is light and fluffy. Add the beaten egg and combine. Stir in almonds, vanilla, cinnamon and nutmeg. Spoon the mixture into the baked tart shell and top with the quartered figs. Bake the tart for 25 minutes or until golden brown.
To make the sauce, in a saucepan combine the red wine, figs, sugar and cinnamon stick. Bring to a boil and simmer until the wine is reduced by half.
Remove the cinnamon stick and transfer the sauce to a blender and puree. Strain into a saucepan and simmer until lightly thickened. Let cool 1 to 2 minutes.
Brush the sauce over the tart and serve with more sauce on the side.
Suggested wine: Bukkuram, Moscato Passito di Pantelleria