Preheat the oven to 175°C (350°F) and grease a 23 cm (9-inch) removable-bottom or springform pan. Mill the spelt berries using the finest setting of your grain mill to make fresh flour.
In a small bowl, whisk together the fresh flour, baking powder, baking soda, cinnamon, and salt. Set aside. In a large bowl, cream the butter and sugar together until the mixture becomes pale and fluffy. Add the eggs, one at a time, beating briefly after each addition, just until incorporated. Gradually fold in the dry ingredients, mixing gently until combined.
Add the grated carrots and gently fold them into the batter with a spoon or spatula. The batter will be quite thick. Transfer the batter to the prepared pan and spread it evenly.
Bake the cake for 50 minutes, or until a toothpick inserted into the center comes out clean. For an extra check, you can use an instant-read thermometer; the internal temperature should read around 95°C (203°F).
Once baked, remove the cake from the oven and place the pan on a cooling rack for about 15 minutes. Carefully run a knife around the edges to loosen the cake, then flip it onto the cooling rack to cool completely. Allow the cake to cool fully before frosting. If you plan to frost it on a different day, wrap the cooled cake tightly to prevent it from drying out.