Line a 8x8" baking dish with foil or parchment paper, spray with non stick spray. Preheat oven to 350 degrees.

In a small bowl, beat the cream cheese till smooth and creamy. Beat in the sugar, scraping down the sides of the bowl a few times with a rubber spatula.

Add the egg and vanilla, beat till just blended. Set aside

For batter: In a mixing bowl, whisk together the melted butter and brown sugar. Add the egg and vanilla and whisk till well combined.

Whisk together the flour, cinnamon, baking powder, and salt in a small bowl. Stir into the wet ingredients.

Fold in the grated carrots.

Spread about 2/3 of the batter into the prepared pan.

Pour the filling over the top of the batter. Drop remaining batter by spoonfuls over the filling. Swirl with a butter knife.

Bake in preheated oven at 350° for about 40 minutes, or until a toothpick inserted in the middle comes out clean.

Cool completely, then cover and chill for at least an hour. Cut into squares.