Preheat your oven to 350°F (175°C). Line a 9x5-inch loaf pan with parchment paper, leaving enough overhang on the sides for easy lifting later.
In a large bowl, whisk together the vegetable oil and both sugars for about 30 seconds until they combine into a wet, sandy mixture.
Beat in the eggs, one at a time, until they are fully mixed in. Stir in the vanilla extract.
In a separate bowl, sift together the flour, baking powder, baking soda, cinnamon, nutmeg, allspice, cloves, and salt. This step helps create a lighter cake texture.
Using a large spatula or wooden spoon, gradually add the sifted dry ingredients to the wet mixture, alternating with the sour cream and milk. Start and end with the dry ingredients. Mix just until a few streaks of flour remain—be careful not to overmix to ensure your cake stays tender!
Gently fold in the freshly grated carrots. Remember, using fresh carrots adds wonderful moisture and flavor!
Transfer the batter to your prepared loaf pan and smooth the top with a spatula if needed.
Bake in the center of your oven for 55 to 60 minutes. The top should be golden brown, and a toothpick inserted into the center of the cake should come out clean or with a few moist crumbs. If the top starts browning too quickly, loosely cover it with a piece of aluminum foil for the last 10-15 minutes. Avoid overbaking to prevent a dry cake!
Remove the loaf from the oven and let it cool in the pan for about 30 minutes. Then, use the parchment paper to carefully lift it out and place it on a wire rack to cool down completely. This is key before adding the glaze!
While the cake cools, beat the very soft cream cheese with an electric hand mixer. Gradually add the powdered sugar, followed by 2 tablespoons of milk. Continue mixing until the glaze is smooth and pourable. If it's too thick, add more milk; if too thin, add more powdered sugar.
Once your carrot cake loaf is fully cooled, pour or drizzle the silky cream cheese glaze over the top, allowing it to drip attractively down the sides. Let it sit at room temperature for 15-20 minutes to set slightly before slicing and savoring your delicious, moist creation!