Preheat the oven to 350°F. Place the flour in a mixing bowl. Add the baking powder, whisk to combine, and set aside. Grease a 9-inch round cake pan. Line the base and side of the cake pan with parchment paper. Place the brown sugar and 3½ tablespoons of the butter in a small saucepan over low heat. Cook, stirring, until the butter and sugar have melted together, about 5 minutes. Carefully, as it will be very hot, pour the brown sugar mixture into prepared cake pan.