Preheat the oven to 180°C. Grease your baking pan with butter and dust with flour to prevent sticking.
Grate the carrots and squeeze out as much liquid as possible. Measure the carrots after removing the liquid to avoid adding excess moisture, which could cause the cake to sink.
In a mixing bowl, whisk together all the dry ingredients: all-purpose flour, baking powder, cinnamon, nutmeg, and salt. If adding other spices, include them here.
In a separate bowl, whisk the liquid ingredients—vegetable oil, full-fat milk, and vanilla extract—until smooth and combined.
In a large mixing bowl (or the bowl of a stand mixer with a whisk attachment), add 3 eggs and beat on high speed for 3–5 minutes, until the eggs become pale and fluffy.
Gradually add the brown sugar to the whipped eggs, and continue whisking on high speed for another 3–5 minutes, until the sugar is fully incorporated and the mixture is light and airy.
With the mixer on low, slowly pour in the prepared liquid ingredients, blending until well incorporated.
Add the dry ingredients to the batter in three parts, folding gently with a silicone spatula after each addition until just combined.
Fold the grated, squeezed carrots into the batter with a silicone spatula, ensuring there are no lumps of carrots or streaks of flour.
Pour the batter into the prepared baking pan(s). Bake for 20-25 minutes, or until a toothpick inserted in the center comes out clean.