Carrot Cake Bars

Preheat oven to 375°F. Line a 9-inch-square baking pan with parchment paper, allowing the parchment to extend over the sides by at least 2 inches. Whisk oat flour, baking powder, salt, cinnamon and cloves together in a small bowl.

Microwave butter in a large microwave-safe bowl just until melted, about 30 seconds. Whisk in brown sugar until combined. Add egg, egg yolk and 1/2 teaspoon vanilla; whisk until combined. Add the flour mixture and whisk just until the dry ingredients are moistened. Fold in carrot. Transfer the batter to the prepared baking dish. Bake until golden brown and slightly puffed and a toothpick inserted in the center comes out almost clean with a few moist crumbs, 25 to 27 minutes. Let cool completely in the pan on a wire rack, about 1 hour.

Meanwhile, beat cream cheese and yogurt in a medium bowl with an electric mixer on medium speed until smooth and creamy, about 30 seconds, scraping down the sides and bottom of the bowl as needed. Add confectioners' sugar and the remaining 1/2 teaspoon vanilla and beat until completely smooth, about 30 seconds.

Use the parchment paper to remove the cooled bars from the pan. Place the bars on a plate or platter; discard the parchment. Spread the frosting evenly over the bars and top with walnuts.