Preheat your oven to 180°C (fan 160°C). Line a 23cm square baking tray with parchment paper, letting the paper hang over the edges like handles. The kitchen will smell warm and inviting as the oven heats up.

Whisk the dry ingredients together. In a large bowl, combine the flour, baking powder, bicarbonate of soda, cinnamon, nutmeg and salt. Whisk until the spices are evenly distributed and the mixture looks pale and uniform, like fine sand.

Add the wet ingredients. Crack the eggs into the dry mixture, then pour in both sugars, the oil and the vanilla. Stir with a wooden spoon until you see a thick, glossy batter form — it should look like a rich caramel colour and smell sweetly of vanilla.

Fold in the carrots and walnuts. Tip in the grated carrots and walnuts, then fold gently. The batter will turn a warm orange as the carrots disperse, and you'll see tiny flecks of carrot throughout. Stop folding as soon as you can't see any flour streaks — the batter should be thick and slightly lumpy.

Bake the cake. Pour the batter into the prepared tray and spread it evenly with a spatula. Bake for 28-32 minutes, until the top is golden brown and springy to the touch. A skewer inserted into the centre should come out clean or with a few moist crumbs attached. The kitchen will smell of cinnamon and toasted nuts.

Cool completely. Let the cake cool in the tray for 10 minutes, then lift it out using the parchment handles and transfer to a wire rack. You'll hear a faint crackling sound as the cake settles. Leave it to cool completely — this takes about 30 minutes — before frosting.

Make the cream cheese frosting. In a clean bowl, beat the cream cheese and butter together until smooth and fluffy, about 2 minutes. The mixture should look pale and feel light. Gradually add the sifted icing sugar and vanilla, beating until the frosting is thick, creamy and spreadable. It should hold its shape when you lift the beaters.

Frost the cake. Spread the frosting evenly over the cooled cake with a palette knife or the back of a spoon. Drag the knife across the top to create gentle swirls — the frosting should look smooth and velvety, with a slight sheen.