In a medium saucepan, combine the granulated sugar with the water and cook over moderately high heat, stirring, until it boils vigorously and the sugar is completely dissolved. Add the cranberries and cinnamon sticks. Cover and cook over moderate heat for 3 minutes, stirring once or twice. Remove the pan from the heat and let the cranberries cool to room temperature. Remove the cinnamon sticks and drain the cranberries well; reserve the cranberry syrup.

While the cranberries cool, prepare the crust. Mix butter, brown sugar, cinnamon, salt, and pecans in a medium bowl. Add flour and stir until just blended. Press the dough evenly over the bottom and up the sides of a 9 1/2-inch tart pan with a removable bottom. Generously prick the bottom and sides with the tines of a fork. Bake in the lower third of an oven preheated to 350° F until the crust begins to feel set, about 15 minutes. Set aside.

In a medium bowl, beat the eggs with the brown sugar, flour, and bourbon. Gently stir in the cream. Spread the cranberries in the prepared tart shell. Drizzle 1 tablespoon of the reserved cranberry syrup over the cranberries, and then pour in the brown sugar custard through a strainer.

Bake the tart in the lower third of an oven preheated to 350° F until the filling looks mostly set in the center and is puffed and pale golden around the edges, about 35 to 40 minutes.

Transfer the tart in the pan to a rack to cool completely, about 2 hours. Pipe or spread lightly sweetened whipped cream on top of the tart before serving. Serve with reserved cranberry syrup.