Begin by preheating your oven to 350 degrees Fahrenheit and positioning the two oven racks, one in the upper middle and one in the lower middle position. Next, line two baking sheets with parchment paper to prepare for baking.
Using a stand mixer set to medium speed, beat the butter and sugar together until they become light and fluffy. This should take approximately 5 minutes.
Next, add the egg and vanilla to the mixture, and continue to beat until well incorporated. Remember to scrape down the sides of the bowl to ensure all ingredients are evenly mixed.
In a large bowl, combine the baking soda, flour, and salt. Then, reduce the mixer speed to low. Gradually add the dry ingredients to the butter mixture, adding 1/2 cup at a time and alternating with the milk. Be sure to begin and end with the flour to ensure even mixing.
Using a 1/4 cup measuring cup, scoop the batter onto baking sheets, leaving a 2-inch space between each cake. This should yield 12 cakes. If you prefer smaller cakes, use a 2-tablespoon measuring spoon and prepare an additional baking sheet.
Bake the cakes at 350 degrees Fahrenheit for 15 to 18 minutes, making sure to switch the baking sheets halfway through for even baking. If you are making smaller cakes, reduce the baking time to 10 to 12 minutes.
To check if the cakes are fully baked, insert a cake tester into the center of one cake; if it comes out clean, they are ready. Keep in mind that the cakes will still be soft. Remove the cakes from the oven and transfer them to a cooling rack to cool completely.