Preheat the oven to 180°C/350°F. Grease and flour a 9-inch square cake pan.
Cream sugar (1 cup) and butter (1/2 cup) together in a mixing bowl. Add eggs (2), one at a time, beating briefly after each addition. Mix in vanilla (2 tsps).
Combine flour (1.5 cups) and baking powder (1.75 tsp) in a separate bowl. Add to the wet ingredients and mix well. Add milk (1/2 cup) and stir until smooth.
Pour batter into the prepared cake pan. Bake in the preheated oven until the top springs back when lightly touched, 30 to 40 minutes. Remove from the oven and cool completely. Top with frosting of your choosing.