Prepare the Oven and Pan: Preheat the oven to 350ºF (180ºC). Line a 9 x 13-inch baking pan Note: Alternatively, if you have a non-stick pan, line just the base with parchment paper and liberally grease the sides with soft butter and dust it with a light layer of flour. This will leave your finished cake with smooth sides.Set aside.
Sift and Combine Dry Ingredients: In a large mixing bowl, sift together the flour, baking powder, and baking soda. Whisk in the salt. Set aside.
Combine Sugar and Wet Ingredients: In another large mixing using electric hand beaters or a stand mixer with the paddle or whisk attached, add the sugar, eggs, oil, and vanilla extract. Beat for 1 minute until well combined. Scrape down the sides.
Add Yogurt and Milk: Beat in the yogurt and milk for about 20 seconds until smooth.
Incorporate Flour Mixture: Add half of the flour mixture to the wet ingredients, beat on low speed until just combined, then add the remaining flour mixture and beat on low until fully incorporated, ensuring not to overmix, about 10-15 seconds. Use a spatula to gently incorporate extra flour from the sides of the bowl back into the batter.
Transfer Batter To Tin: Pour the batter into the prepared baking pan, smoothing the top with a spatula.
Bake: Bake for 22-25 minutes, or until a toothpick inserted into the center comes out clean and the top springs back when lightly pressed.
Cool: Allow the cake to cool in the pan for 15 minutes, then remove from pan and cool completely on a wire rack.