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Step 1
First things first, we need to get that 1 lb. cream cheese to room temperature. If you don’t have time to let it sit out on the counter for several hours, cut it into 1" pieces and place on a heatproof plate on top of your stove. Alternatively, you can microwave the plate of cream cheese in 10-second increments until just softened but not melted, about 30 seconds total.
Step 2
Place a rack in middle of oven; preheat to 350°. Lightly grease a 9x5" loaf pan with vegetable oil. Line pan lengthwise with parchment paper, leaving about a 2" overhang. (This will help you lift the cake up and out of the pan.) Important note! If you are using a smaller pan, you're going to need to hold back some batter—you'll need at least a ½" between the batter and the lip of the pan to account for oven rise, otherwise your cake will overflow. You can bake remaining batter in muffin tins if you have them.
Step 3
Whisk 2¼ cups all-purpose flour, 2 tsp. baking powder, 2 tsp. ground ginger, ¾ tsp. baking soda, 2 tsp. cinnamon, and 1½ tsp. Diamond Crystal or (1 tsp. Morton) kosher salt in a medium bowl.
Step 4
Peel ¾ lb. carrots and cut off knobby end. Grate on the large holes of a box grater right into bowl of dry ingredients. Use your hands to toss until well coated.
Step 5
Scrape half of cream cheese into a large bowl. (This is for the batter, the other half is for the icing!) Using a spatula, spread cream cheese around sides of bowl, working it a few times with your spatula to help soften. Add 1½ cups sugar and keep working with spatula to completely incorporate until it’s no longer gritty all sugar is dissolved, about 15 seconds. Crack 2 large eggs into bowl, then whisk until mixture is very smooth. It might look separated and chunky at first, but whisk vigorously and it will eventually come together. Slowly stream in ¾ cup vegetable oil, whisking constantly to homogenize. Add 2 tsp. vanilla extract and whisk again to combine.
Step 6
Fold dry ingredients into egg mixture with your spatula until almost no streaks of floury bits remain.
Step 7
Scrape batter into prepared pan, smoothing top with the back of a spoon or spatula.
Step 8
Bake cake until a tester inserted into the center comes out clean, 80–90 minutes. (Baking time will vary depending on the size and shape of your loaf pan, so if you aren't using a standard 9x5", start checking for doneness at the 70-minute mark and keep an eye on things.) Let cool 20 minutes, then remove from pan using parchment overhang. If the edges are sticking, slide a butter knife around the edge to help release. Transfer to a wire rack and let cool completely.
Step 9
While cake cools, make your icing. Scrape remaining 8 oz. cream cheese into a medium bowl. Similarly to what you did earlier, use a spatula to work it around sides of bowl. Add remaining ¼ cup sugar, 1 tsp. vanilla, and ¼ tsp. Diamond Crystal (or a pinch of Morton) kosher salt. Mix with spatula to bring everything together, paddling it as necessary, until icing is very smooth and shiny. (This will take some elbow grease, but don't give up!) Cover and keep chilled until cake has cooled.
Step 10
Place cooled cake on a platter. Dollop cream cheese frosting on top and make swirls and swooshes with the back of a small spoon as you spread it out to make it look cute. Dust lightly with more cinnamon. Slice with a sharp chef’s knife (not a serrated one) to serve.