Preheat oven to 375. Spray a 13x4-inch rectangular tart pan with removable bottom or a 9-inch round tart pan with removable bottom.
In the bowl of a stand mixer fitted with the paddle attachment, cream together the butter and sugar at medium-high until very light and fluffy, about 3 minutes. In a separate bowl, stir together the flour, baking powder, and ginger. Turn down your mixer and incorporate the flour mixture into the butter mixture until combined, scraping the sides and bottom of the bowl as needed. Mixture will be very crumbly.
Pour the crumbly mixture into the tart pan. Press the dough evenly and firmly into the pan and into the scalloped grooves. Place the tart pan on a sheet pan. Bake for 20 minutes until set and golden on the edges.
Just shortly before the shortbread is ready (about 5-7 minutes before), melt the butter in a small saucepan with the Golden Syrup. When it is melted and bubbling, quickly whisk in the powdered sugar and ginger, stirring until smooth. Pour the glaze over the shortbread as soon as it comes out of the oven, spreading it to cover the shortbread entirely. Immediately sprinkle the top of the glaze with fine sea salt and crystallized ginger. Allow the glaze to set for about 20 minutes. Remove the shortbread from the pan while still warm and gently slice into bars.