Preheat oven to 190°C/170°C fan-forced. Grease 2 x 20cm (7cm deep) round cake pans. Line bases with baking paper. Line a baking tray with baking paper. Place pecans on tray and bake for 5 minutes or until toasted. When cool enough to handle, roughly chop pecans.
Meanwhile, place flour, baking powder, salt, mixed spice and ginger in a large bowl and stir to combine. Make a well in the centre.
Place oil, sugars, vanilla and eggs in a medium bowl, then whisk until combined. Add wet ingredients to dry ingredients and stir until just combined. Fold in carrot and half of the pecans.
Divide batter between pans, then bake for 30 minutes or until skewer inserted into centres comes out clean. Stand until completely cool.
Meanwhile, to make the cream cheese icing, add cream cheese to the bowl of a stand mixer fitted with a paddle attachment and beat on medium speed until smooth. Add icing sugar and vanilla, then beat until well combined. Sandwich cakes using half of the icing, allowing icing to overhang around edge. Top with remaining icing, then scrape sides smooth. Scatter over remaining pecans and serve.