Preheat your oven to 350°F (175°C). Line an 8×8-inch baking pan with parchment paper, leaving a 2-inch overhang on two sides for easy removal. Lightly grease the parchment with a little butter or nonstick spray.

Wash, peel (optional), and grate enough carrots to measure 1 cup. Use the fine side of a box grater for a more evenly textured batter.

In a medium bowl, whisk together the flour, cinnamon, nutmeg, baking powder, and salt until evenly combined.

In a separate large bowl, cream the butter with light brown sugar until light and fluffy. Add an egg and vanilla extract, beating until combined.

Fold the dry ingredients into the wet mixture, stirring gently until just combined. Fold in the grated carrots until evenly distributed.

In a small bowl, beat the cream cheese with granulated sugar and egg yolk until smooth and silky.

Spread about two-thirds of the carrot batter into the prepared pan, smoothing it into an even layer.

Dollop spoonfuls of the cream cheese mixture over the batter. Drop the remaining carrot batter in spoons across the pan and gently swirl.

Bake at 350°F for 28–35 minutes, or until the cream cheese swirl is set and the cake portion springs back slightly to the touch. Test with a toothpick for doneness.

Cool the pan on a wire rack for at least 30 minutes, then lift the bars out using the parchment overhang and let cool completely before slicing.

Dust lightly with powdered sugar or drizzle a simple glaze, or sprinkle chopped nuts on top right after baking.