Preheat the oven to 180°C conventional or 160°C fan-forced. Lightly grease a 20 cm round cake tin, at least 6 cm deep, and line the base and sides with baking paper.
Zest the oranges before juicing them. Place the caster sugar and orange zest in a large bowl and whisk well to combine and to remove any clumps of zest.
Add the eggs and whisk until combined. Whisk in the Greek yoghurt, oil, orange juice and vanilla until smooth. A brief whisk is enough - there’s no need to beat until fluffy.
In a separate bowl, whisk together the plain flour, almond meal, baking powder, bicarbonate of soda and salt. Break up any lumps of almond meal.
Add the wet mixture to the dry ingredients. Gently fold with a spatula, scraping the base and sides of the bowl, until no dry flour remains. Stop once combined.
Pour the batter into the prepared tin and tap 2–3 times on the bench to release air bubbles. Bake on the middle shelf for approximately 30–35 minutes. The cake should be golden, the centre should spring back lightly when touched, and a skewer inserted into the centre should come out clean.
Leave in the tin for 15 minutes, then carefully transfer to a wire rack to cool completely. Dust lightly with icing sugar just before serving.