Preheat your oven to 165°C (330°F). In a mixing bowl, beat the eggs, salt, and vanilla on high speed for a few minutes.
Add the brown sugar and granulated sugar, then mix again on high until the mixture is light and fluffy.
Add the oil and pumpkin purée, mixing just until combined.
In a separate bowl, whisk together the flour, baking soda, baking powder, cinnamon, and pumpkin spice. Add this dry mixture to the wet ingredients and mix on low or with a hand whisk until just combined. Do not overmix.
Pour the batter into a greased mold. Bake at 165°C (330°F) for about 25 minutes, or until the tops are golden brown. I like to bake with fan and bottom element on, with the tray placed in the middle of the oven.
For the Glaze
Whisk together the cream cheese, powdered sugar, milk, and pumpkin spice until smooth. Spread or drizzle over the cakes once they have cooled slightly.
Video
Notes
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The mixer model I have linked is from the same brand but a newer model than the one I have, I couldn't find the one I have.