Preheat the oven to 320°F/160°C and line a muffin pan with paper liners, and set aside.
In a small bowl, combine the cake flour, all-purpose flour, baking soda, baking powder, salt, and spices. Set aside.
In a separate bowl, combine the eggs, sugar, oil, greek yogurt, and vanilla extract.
Add the flour mixture and grated carrots and mix until just combined.
Scoop out the batter evenly and bake for 18 to 20 minutes. Let them cool in the pan for a couple minutes before taking them out to a wire rack to cool completely.
Frosting
In a bowl, beat the unsalted butter until it becomes fluffy. Add the cream cheese and continue to beat.
Beat in the powdered sugar and lemon zest.
Put the frosting into a piping bag and frost the cupcakes to your liking.