Preheat oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking pan.
Whisk flour, baking powder, and salt together in a bowl. Beat brown sugar, butter, eggs, and 1 tablespoon vanilla extract together in a bowl using an electric mixer until smooth and creamy. Stir flour mixture into creamed butter mixture until batter is well combined and thick; spread into the prepared baking pan.
Combine white sugar, 2 tablespoons cinnamon, and ginger together in a bowl; sprinkle over batter.
Bake in the preheated oven until blondies are beginning to pull away from the sides of the pan and are set in the middle, 25 to 30 minutes. Allow blondies to cool, at least 30 minutes.
Beat confectioners' sugar, cream, 1 tablespoon cinnamon, and 1 teaspoon vanilla extract together in a bowl until glaze is smooth; drizzle onto blondies.