Preheat oven to 350°F. Line a 9x13 baking pan with parchment paper.
In a bowl, whisk melted butter, brown sugar, and granulated sugar until smooth. Mix in eggs and vanilla.
Stir in flour, baking powder, cinnamon, nutmeg, and salt just until combined. Fold in grated carrots.
In a separate bowl, beat cream cheese, sugar, egg, and vanilla until creamy and smooth.
Spread half the carrot cake batter into the pan. Gently spread the cream cheese layer on top, then finish with the remaining carrot cake batter.
Bake for 35–40 minutes until set around the edges and slightly soft in the center. Cool completely before slicing.
