Preheat your oven to 350°F. While it heats, measure out all your dry ingredients (flour, baking powder, salt, cinnamon, nutmeg, and ginger) into a bowl and whisk them together—this aerates the dry ingredients and distributes the leavening agent and spices evenly. Finely grate your carrot (you should have about 1/2 cup packed) and zest your orange. Set everything aside. I like to use a microplane for the orange zest because it gives you the bright citrus oils without any bitter white pith.

In a separate bowl, whisk together the room-temperature egg, brown sugar, vegetable oil, and vanilla until the mixture is well combined and slightly pale—this takes about 1 minute of whisking. The room-temperature egg incorporates more evenly into the batter, creating a better texture. Fold in the grated carrot and orange zest until just combined, making sure the carrot is distributed throughout.

Pour the wet ingredient mixture into the bowl with the dry ingredients and fold gently with a spatula until just combined—do not overmix, as this can develop gluten and make the cakes tough. A few small lumps are perfectly fine; the batter should come together in about 10-15 gentle folds. Stop as soon as you don't see streaks of dry flour.

Lightly grease two 6-8 oz ramekins with butter or cooking spray and divide the batter evenly between them, filling each about three-quarters full. Place them on a baking sheet (for easier handling) and transfer to your preheated 350°F oven. Bake for 28-32 minutes, until a toothpick inserted into the center comes out clean or with just a few moist crumbs—start checking at 28 minutes to avoid overbaking. The cakes will be set on the edges and slightly tender in the center when done.

While the cakes bake, prepare the frosting so it's ready when they cool. In a clean bowl, beat the softened cream cheese and butter together until smooth and creamy, about 1 minute. Sift in the powdered sugar (sifting prevents lumps in your frosting) and add the vanilla and a pinch of salt. Beat until light and fluffy, about 1-2 minutes. I find that sifting the powdered sugar directly into the mixture and beating it in prevents those grainy texture issues that can happen with cream cheese frosting.

Remove the cakes from the oven and let them cool in their ramekins for 5-10 minutes—this brief rest allows them to set slightly so they won't crumble when you handle them. You can serve them warm in the ramekins or turn them out onto plates once they've cooled a bit. Top each cake with a generous dollop of the cream cheese frosting from Step 5 while the cakes are still slightly warm (the warmth will soften the frosting slightly and help it meld with the cake). Serve immediately.