Preheat the oven to 325°F. Generously butter a square 8-inch pan. You can also line the pan with parchment paper with an overhang and grease the paper.
½ tablespoon butter
In a large bowl, whisk together the eggs, oil, and stevia until combined.
4 large eggs, ½ cup avocado oil, 1 ½ teaspoon stevia glycerite
Mix in the almond flour using a rubber spatula and then a hand whisk. Whisk until completely smooth.
1½ cup superfine almond flour
Whisk in the cinnamon, allspice, kosher salt, and baking powder.
Transfer the batter to the prepared pan, smoothing it out with a rubber spatula. Bake the cake until puffed and fragrant and a toothpick inserted in its center comes out clean, about 25 minutes.
Cool the cake in the pan on a cooling rack until completely cool, about 1 hour.
When the cake is completely cool, make the frosting: whisk the soft cream cheese, stevia, and vanilla with a hand whisk until smooth and fluffy.
8 ounces cream cheese, 1 ½ teaspoon stevia glycerite, ½ teaspoon pure vanilla extract
Run a knife around the edges of the pan to loosen the cake. Cut the cake into nine squares. To remove each square from the pan, firmly slide a cake server underneath each slice and lift it out.
Using a soup spoon, divide the frosting evenly between the cake slices. Use a small spatula to spread the frosting evenly on top of each slice (just like you would frost a cupcake).
Video
Notes
A granulated sweetener in the frosting will feel grainy, so please use a powdered sweetener. If using a powdered sweetener in the frosting instead of stevia, it's possible that you would need to add a bit more heavy cream to get the right consistency.
Sweetness is a personal preference. Use these amounts as a guide and adjust to taste.
Ideally, you would grate the carrots finely by hand or in a food processor. But I often buy pre-shredded carrots. I give them a quick extra chop before using them since they tend to be shredded pretty coarsely.
Keep in mind that coarsely shredded carrots will affect the cake's texture - they cook "al dente" inside the cake. I like this texture. But if you want a softer and more uniform texture, use finely grated carrots.
Once completely cool, you can keep the leftovers in an airtight container in the fridge for up to 5 days. Remove them from the fridge about 30 minutes before enjoying them. Like any other spice cake, this one improves with time. It's moister and more flavorful the day after you bake it.
You can also freeze this cake, provided it is not frosted. Once frosted, I don't recommend freezing it.