To make the waffles: Preheat a waffle iron according to the manufacturer's instructions.

Whisk flour, white sugar, baking powder, and 1 teaspoon salt together in a large bowl. Beat warm milk, 1/3 cup melted butter, eggs, and 1 teaspoon vanilla extract together in another bowl. Add milk mixture to flour mixture and stir until batter is lumpy and just moistened.

Ladle batter into the preheated waffle iron, working in batches if necessary, and cook until golden brown and the iron stops steaming, about 5 minutes.

To make the cinnamon topping: Stir brown sugar, 1/2 cup melted butter, and cinnamon together in a small bowl.

To make the cream cheese topping: Beat confectioners' sugar, cream cheese, 1/4 cup softened butter, 1/2 teaspoon vanilla extract, and 1/8 teaspoon salt together in a medium bowl.

Place waffles on a plate and drizzle cinnamon mixture and cream cheese mixture over the top.