Maple-Walnut Cake with Brown-Sugar Frosting

Nonstick cooking spray

all-purpose flour (spooned and leveled), plus more for pans

baking powder

fine salt

unsalted butter, room temperature

packed dark-brown sugar

large eggs

pure maple syrup

whole milk

chopped walnut halves, toasted

cream cheese, room temperature

unsalted butter, room temperature

packed dark-brown sugar

confectioners' sugar