Heat the oven and prep the pan: Preheat to 350°F (175°C). Butter the 8-inch pan, line the bottom with a parchment round, then butter and flour the sides — tap out the excess.
Cream the butter and sugar: Beat the 12 tbsp butter and 1 cup sugar with the mixer for 3 to 4 minutes until pale, fluffy and noticeably lighter in color.
Beat in the eggs and vanilla: Add the 3 beaten eggs a little at a time, beating well after each addition. Stir in the 1 tsp vanilla extract.
Fold in the flour: Sift the 1 1/2 cups flour with the 1 1/2 tsp baking powder and 1/4 tsp salt. Fold into the batter in two additions — gentle strokes. Add 2 to 3 tbsp milk until the batter falls off the spoon in a slow, thick ribbon.
Bake the sponge: Pour into the pan, smooth the top, tap once on the counter. Bake 25 minutes, until golden and springy, toothpick clean. Cool 10 minutes in the pan, then turn out onto the wire rack and cool completely — at least 45 minutes.
Make the ganache while the sponge bakes: Put the 7 oz chopped chocolate and 4 tbsp butter in the heatproof bowl. Heat the 1 1/4 cups cream and 2 tbsp golden syrup until just simmering. Pour over the chocolate, rest 2 minutes, then stir from the center outward until thick and glossy. Set aside ~30 minutes until spreadable.
Whip the ginger cream: Whip the chilled 1 1/4 cups cream with the 2 tbsp powdered sugar to soft peaks. Fold in the grated ginger, juice and all. Taste for warm heat behind the sweetness.
Torte and assemble: Once the sponge is completely cool, slice it horizontally into two even layers. Spread the ginger cream over the bottom layer right to the edges, set the top layer on, press lightly.
Glaze and set: Pour or spoon the thickened ganache over the top and spread to the edges, then smooth the sides. Let set 20 to 30 minutes at room temperature before slicing.