Preheat the oven to 175°C. Lightly grease an 8x8-inch square pan with some butter and dust with flour, set aside.
Use an electronic mixer to beat the butter and sugar (med-high speed) until well combined or pale yellow in color, about 3 minutes.
Turn the mixer to low speed and add in the first egg, beat well after each addition of egg until creamy, about 1 to 2 minutes each.
Scrape down the sides for even mixing. Add in the vanilla extract and mix well. Sift and fold in the flour in three batches and mix well.
Lastly add in the whole milk and plain yogurt.
Pour the batter into the greased baking pan. Shake it lightly to distribute the cake batter evenly. Bake until golden brown and cooked, about 40 - 50 minutes. To prevent the top of the cake from over browning, cover the top of the baking pan with a sheet of aluminum foil once the cake top is set. Use a cake tester to test doneness.
Remove it from the oven and let cool on the wire rack for 5 minutes. Cut into pieces and best served warm.