Bake and cool the torta margherita the day before assembling the cake, if possible, to make the layer easier to slice.
For the syrup, combine the sugar and water in a small saucepan, bring to a boil over low heat, and cool. Stir in the liqueur.
For the macaroon topping, break the almond paste into 1-inch pieces and place in the bowl of a heavy-duty mixer fitted with the paddle or in a food processor fitted with the metal blade. Add one egg and mix on lowest speed or pulse in with the processor. After the first egg is almost absorbed, add the second and beat or process until smooth. Add the liqueur and work smooth again. Cover the topping until assembling the cake to prevent it from crusting.
To assemble, slice the torta margherita into 2 equal layers, slicing horizontally through the center of the cake. Invert the top layer onto a cardboard disk or a heat-proof platter so that what was the top of the cake as it baked is now facedown on the cardboard. Moisten with half the syrup, using a brush. Spread the layer evenly with the ¼ cup jam.
Moisten the cut surface of the remaining layer with half the remaining syrup and invert it onto the jam. The top surface of the cake is now what was the bottom as it baked. Moisten with the remaining syrup.
Spread 2 tablespoons of the macaroon topping around the sides of the cake, so that the piped macaroon mixture will adhere to it and not fall off. Place half the remaining mixture in a pastry bag fitted with a ¼-inch star tube (Ateco #1) and pipe a series of vertical lines against the sides of the torta. The lines should touch and cover the entire outside of the cake. Pipe the remaining macaroon mixture on the top of the torta in a series of horizontal lines that touch each other. Last, pipe a border at the top edge of the cake where the piping on the top and sides meet. See the illustration for help with the piping. Chill the torta.
Preheat the oven to 425 degrees. Place the chilled torta on a stack of 3 or 4 jelly roll pans or cookie sheets; using several will insulate the bottom of the cake and prevent it from heating. If using jelly roll pans, invert the stack so that the cake lies on the back of a pan for easy removal afterward. Place the torta in the middle level of the oven. Bake for about 10 minutes, until the macaroon topping is a deep golden color. Turn the pans or sheets frequently so that the topping colors evenly. Remove from the oven and leave on the pans or sheets.
Heat the corn syrup and vanilla to boiling and use a soft brush to glaze the still-hot surface of the topping. An atomizer also works very well for glazing the topping. Remove the torta from the pans or sheets and cool on a rack. Keep loosely covered with aluminum foil at room temperature or refrigerate. If you refrigerate the torta, bring it to room temperature before serving.