2 1/2 cups (about 27 ounces) fig preserves or jam (see Note)
1 teaspoon milk
Vanilla ice cream, for serving
In a food processor, grind the pecans and sugar until the nuts are very fine. Sift together the flour, baking powder and cinnamon. In a medium bowl, using an electric mixer, beat the butter with the pecan mixture until light and fluffy. Add 2 of the eggs and the vanilla and beat until smooth. Using a wooden spoon, stir in the dry ingredients in 3 batches, mixing until the flour is incorporated; the dough will still be sticky.
Divide the dough in half. Pat 1 half into a 6-inch disk for the tart base and wrap it in wax paper. Roll the remaining dough into a log and cut it in half crosswise. Pat 1 of the pieces into a 5-inch disk for the lattice top and wrap it in wax paper. Cut the remaining dough log in half again and wrap each piece separately; these will form the sides. Refrigerate all of the dough until thoroughly chilled, at least 2 hours or overnight.
Preheat the oven to 375°. Line the bottom of a 9-by-2 1/2-inch springform pan with a round of parchment paper. On a lightly floured surface, roll the 6-inch disk into a 9-inch round and fit it into the bottom of the pan. Using your hands, roll each small piece of the dough log into a 13-inch long rope. Fit the ropes into the pan around the base and join the ends to make one continuous rope. Evenly press the dough 1 1/2 inches up the sides of the pan to form a seamless shell. On a sheet of wax paper, roll the remaining disk into a 9-inch round, then transfer it to a rimless baking sheet and refrigerate.
Spoon the fig preserves into the tart shell. The filling should come almost to the top of the pastry. Cut the chilled round of dough into 1/2-inch-wide strips; lay them, lattice-fashion, on top of the preserves and anchor them to the dough rim. Lightly beat the remaining egg with the milk and brush on the lattice. Bake the tart on the bottom shelf of the oven for about 50 minutes, or until the lattice is golden. Let cool on a rack before removing the sides of the pan. Serve with vanilla ice cream.
This tart can be made with thick, sweet Kadota Fig Preserve.