Preheat oven to 350 degrees F (175 degrees C). Line a 9x13-inch baking pan with parchment paper, leaving a 1-inch overhang over each side.

Combine brown sugar and butter in a large bowl; beat with an electric mixer until light and fluffy. Beat in eggs and vanilla extract.

Whisk flour, baking powder, and salt together in a separate bowl. Beat flour mixture gradually into the creamed butter mixture until batter is combined. Spread batter in the bottom of the lined baking pan.

Mix white sugar and cinnamon together in a small bowl. Sprinkle 2 tablespoons of the cinnamon sugar over the batter.

Bake in the preheated oven until edges are light brown, 25 to 30 minutes. Transfer to a wire rack to cool completely, about 15 minutes.

Spread dulce de leche over cooled crust.

Combine white chocolate, heavy cream, and light corn syrup in a small saucepan. Cook and stir over low heat until smooth, about 5 minutes. Let cool slightly, about 5 minutes.

Spread white chocolate mixture over dulce de leche. Sprinkle remaining cinnamon sugar on top. Cover baking pan and refrigerate until firm, at least 1 hour.