Preheat the Oven: Preheat your oven to 350°F (175°C). Grease and flour one 8-inch round cake pan or line it with parchment paper.
Mix Dry Ingredients: In a medium-sized bowl, whisk together 1 ¼ cups flour, 1 ¼ teaspoons baking powder, and ¼ teaspoon salt. Set aside.
Cream Butter and Sugar: In a large bowl, beat together ⅓ cup softened butter and ¾ cup sugar using an electric mixer until light and fluffy (about 2-3 minutes).
Add Eggs and Vanilla: Add 2 large eggs one at a time, beating well after each addition. Then, stir in ½ tablespoon vanilla extract.
Combine Dry and Wet Ingredients: Gradually add the dry ingredients into the butter mixture, alternating with ½ cup milk. Start and end with the dry ingredients. Mix gently until just combined—don't overmix.
Pour and Bake: Pour the batter into the prepared pan, smoothing the top with a spatula. Bake in the preheated oven for 20-25 minutes, or until a toothpick inserted into the center comes out clean.
Cool: Allow the cake to cool in the pan for about 10 minutes. Then, remove it from the pan and transfer it to a wire rack to cool completely.
Serve: Once cooled, you can frost or serve as is. Enjoy your homemade cake!