Preheat oven to 180°C. Grease the base and sides of a 3cm-deep 30cm x 20cm pan and line it with baking paper.
In a bowl, combine teabags, golden syrup, fresh ginger, and 1 cup (250 ml) of boiling water. Let the ingredients steep for 3 minutes while you squeeze off the extra liquid.
Sift together flour, baking powder, cocoa, ground ginger and mixed spice in a bowl.
In another bowl, whisk the eggs and sugar for 3 minutes, or until the mixture is lighter and the sugar has dissolved. Whisk in oil until fully combined, followed by the tea mixture.
Create a well in the dry ingredients and add the wet ingredients, blending with a wooden spoon only until incorporated (do not overmix). Fill the pan with batter, then smooth with a spatula. Bake the cake for 35 to 40 minutes, or until it springs back to the touch. After 15 minutes, remove from the pan and allow cool fully on a rack.
In a stand mixer with the paddle attachment, combine all the frosting ingredients and blend until smooth. Spread over cake and sprinkle with ginger.