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Preheat the oven to 350 degrees F (175 degrees C). Grease and flour a 9-inch round pan.
Cream sugar and butter together in a mixing bowl with an electric mixer until light and fluffy. Beat in eggs, one at a time, mixing until fully incorporated after each addition. Stir in vanilla.
Combine flour, baking powder, and salt in a mixing bowl. Stir dry ingredients into wet ingredients alternately with milk, adding 1 to 2 tablespoons more milk if batter is too stiff. Spread batter evenly into the prepared pan.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, 30 to 35 minutes. Cool in the pan on a wire rack for 10 minutes.
Turn cake out onto a serving plate and cool to room temperature, 20 to 30 minutes. Dust with confectioners' sugar right before serving.