You do not need baking soda or baking powder in this cake. Eggs are the leavener.
Preheat the oven to 350°F (175 degrees C). (If you haven't calibrated your oven recently, I recommend you calibrate your oven once a year. For info read: How to Calibrate your Oven.)
In the bowl of an electric mixer, cream butter and sugar on medium speed until fluffy. Stop the mixer and scrape the sides. Mix again.
Beat in eggs, one at a time, mixing well after each addition. Stop mixer and scrape sides. Mix again.
Beat in flour alternately with vanilla and milk, mixing just until incorporated. Pour batter evenly into the prepared pan and smooth the top. (This is a thick batter.)
Bake in the preheated 350°F oven until a wooden pick (like a skewer or cake tester, inserted into the thickest part of the cake comes out with moist crumbs or no crumbs. (Watch it closely. Every oven bakes differently. As well the pan you use affects cooking times.) If using a thermometer, the internal temperature of the cake will be 200°F when fully cooked.
When the cake is done cooking, remove it from the oven and use a butter knife to loosen the cake around the edges of the pan as well as the center hole. Set the cake on a wire rack to cool in the pan for 25 to 30 minutes, then turn it out onto a wire rack to cool completely. (I double-flip my cake so that the top is the top.)
Serve warm or cool. Store in an airtight container either on the countertop or fridge.
Notes
*You can use salted or unsalted, your preference.Odd as it may seem, you can actually omit the extract (flavoring). If omitted the cake with have a mellow butter flavor. Originally, the extract wasn't used often because it was expensive and hard to get at times. With that being said, I prefer to add either vanilla or almond extract (or 1 tablespoon of each.).