Preheat the oven to 165°C fan-forced. Grease and line the base and sides of a 22cm round cake tin with baking paper.
Trim the heirloom carrots and halve them lengthways. If any are particularly thick, quarter them lengthways. You want relatively thin pieces so they soften properly while the cake bakes. Anything thicker than 1.5cm is too much. Arrange them in the lined baking tin with the flat part of the sliced carrot facing the tin. The carrots shrink a fair bit in the oven so you want them quite crowded in the tin, about a layer and half of carrots.
Add the butter and brown sugar to a small saucepan over medium heat. Cook, stirring, until the butter has melted and the mixture is bubbling. Add the cinnamon and a pinch of salt, then cook for around 2 minutes until glossy and slightly thickened. If the caramel is splitting, add 1 tablespoon of warm water and whisk briefly to emulsify again.
Pour the caramel over the carrots as evenly as possible. Don't worry if they aren't completely covered, the caramel with spread a lot when baking.
To make the cake batter, add the self-raising flour, plain flour, bicarbonate soda, cinnamon and salt to a large bowl and whisk to combine.
In a separate large bowl, whisk together the brown sugar, olive oil, golden syrup, eggs and vanilla until smooth and well combined.
Add the dry ingredients to the wet ingredients and fold together until just combined.
Fold through the grated carrot and chopped walnuts, taking care not to overmix.
Carefully spoon the cake batter over the arranged carrots, then gently spread it into an even layer without disturbing them.
Bake for 50 - 65 minutes, or until a skewer inserted into the centre of the cake comes out clean.
Leave the cake in the tin for 5–8 minutes. Run a knife around the edge if needed, then place a serving plate over the tin and carefully invert the cake while it's still warm. Gently peel away the baking paper.
Leave the cake to cool while you prepare the whipped cream cheese and caramel sauce.
For the whipped cream cheese, beat the softened cream cheese until completely smooth. Add the icing sugar (sift it if clumpy), vanilla and salt and beat again until combined. With the mixer running on low, gradually add the thickened cream, then increase the speed and whip until thick, smooth and fluffy. Keep refrigerated until ready to serve.
For the salted caramel sauce, add the caster sugar to a small saucepan over medium heat and cook until melted and light amber in colour. Add the butter and whisk until combined.
Carefully pour in the thickened cream, it will bubble vigorously and whisk until you have a smooth caramel sauce. Add a pinch of salt, then remove from the heat and allow it to cool slightly.
Serve slices of the carrot cake with a generous spoonful of whipped cream cheese and warm salted caramel sauce poured over the top.