Grease the Swiss roll tin lightly with oil and line with baking paper. Preheat the oven to 180°C (conventional, not fan).
Place the 80g of sugar and the orange zest into the bowl of a stand mixer. Rub the zest into the sugar using your fingers/the back of a spoon until evenly distributed.
Add the eggs and whisk on high speed until pale, fluffy and tripled in volume (the 'ribbon stage').
While the eggs are whisking, sift the flour, baking powder, spices and salt together into a separate bowl, then whisk in the ground almonds. Set aside.
Once the egg mixture has tripled in volume, add the almond and vanilla extract and whisk again briefly to incorporate.
Sprinkle the dry ingredients over the egg mixture, then use a balloon whisk or large metal spoon to fold them in, until no streaks of flour remain.
Pour the sponge batter into the prepared tin and use an offset spatula to spread it out into an even layer. Bake in the preheated oven for 15-17 minutes, until risen, golden and just firm to the touch.
While the cake is baking, cut a rectangle of baking paper slightly larger than the Swiss roll tin. Spread it out on a clean work surface, then sprinkle over the remaining 2 tbsp caster sugar.
Allow the cake to cool in the tin for 1 minute, then flip it out onto the sugared baking paper. Peel the baking paper off the bottom of the cake, then carefully and tightly roll the warm cake up into a log. Leave the rolled cake at room temperature to cool completely.