For syrup, in a medium saucepan, stir together the 1-1/4 cups sugar, water, fresh ginger, and lemon peel. Bring to boiling; reduce heat. Simmer, uncovered, over medium heat for 30 minutes, stirring occasionally. Remove from heat. Stir in honey, brandy, and lemon juice. Strain to remove lemon peel and ginger. Let syrup cool to room temperature (do not refrigerate).
Preheat oven to 325 degrees F. For filling, in a bowl, combine pistachios, apricots, cherries, 1/4 cup sugar, ground ginger, and cardamom. Set aside.
Brush the bottom of a 3-quart rectangular baking dish with some of the melted butter. Unfold phyllo dough. Cut through the whole stack of phyllo dough sheets at one time to make a 13x9-inch rectangle. Discard extra pieces. Keep phyllo covered with plastic wrap, removing sheets as needed. One sheet at a time, layer 10 phyllo sheets in the dish, generously brushing each sheet with melted butter. Sprinkle one-third of the filling on the phyllo layers. Repeat layering the phyllo sheets and filling twice.
Layer remaining phyllo sheets on the third layer of filling, brushing each sheet with butter before layering the next sheet. Drizzle any remaining butter over the top layer.
Use a sharp knife to make four cuts through all the layers the length of the dish to make five rows. Then make eight diagonal cuts through all the layers, making diamonds. (Do not remove the pieces from the dish).
Bake for 40 to 50 minutes or until golden brown. Slightly cool in the baking dish on a wire rack. Spoon syrup over hot baklava. Cool completely or let stand overnight at room temperature. Place baklava in tin, separating layers with waxed paper; cover.