Gather and measure the ingredients. Cut butter into small pieces and place in a mixing bowl; let stand at room temperature to soften slightly.
Preheat the oven to 180°C and position an oven rack in the lower half of the oven.
Sieve the flour, baking powder, and salt together three times.
Grease the pan with softened butter. Dust lightly with flour and shake off the excess. Set aside.
Cut the butter into small pieces and place in a mixing bowl. Leave the bowl out on your counter until it reaches room temperature (21°C).
Slightly beat the softened butter with a wooden spoon before beating it with the hand mixer.
Next, start beating with a hand mix when the butter is soft enough. Beat on high speed for about 2 minutes.
Start adding the sugar after the butter becomes a bit creamy. Gradually add sugar, a tablespoon at a time. Beat at high speed until the mixture becomes pale yellow or almost white, light, and fluffy for about 5 minutes. And then continue beating at medium-high for about 3 minutes.
Stop the mixer and use a spatula to scrape down the sides of the bowl as needed. Mix until it is light, fluffy, creamy, and become pale yellow.
Lightly whisk the whole eggs, egg yolk, and vanilla extract (if using) together in a small bowl just until combined with a fork.
Add the egg mixture gradually, little by little, and beat at high speed until all the eggs are incorporated.
Beat until thick and fluffy, about 3 to 5 minutes in total, stopping to scrape the bowl as needed.
Alternately add flour mixture and milk to the butter mixture, folding gently with a rubber spatula after each addition until just combined.
Start with 1/3 flour mixture and mix, then 1/2 the milk and mix, then the second 1/3 of the flour mixture and mix, then the remaining milk and mix, finish with the last 1/3 of the flour mixture and mix until combined.
Make sure you keep folding until the batter appears homogeneous without white dots.
Do not over-mix. Stop mixing once the flour is incorporated and homogenous.
Pour the batter into the prepared pan and level the surface evenly with a spatula. Give the cake pan a few taps on the counter to get rid of any large trapped air bubbles.
Bake for 25 mins at 180°C, then reduce oven temp to 170°C. Continue to bake for another 5 to 10 mins or until a wooden skewer inserted into the middle of the cake comes out with a clean crumb.
Let the cake cool in the pan on a wire rack for about 5 to 10 minutes.
Remove the cake from the pan and place it on a cooling rack to cool completely. However, you can also serve this butter cake warm if you like.
Serve & Enjoy! It is a perfect accompaniment to a nice hot cup of tea or coffee.