Preheat your oven to 350°F (175°C). This ensures that the cake bakes evenly.

In a large mixing bowl, combine the yogurt, sugar, and eggs. Whisk together until smooth and well combined. This will create a light and airy batter.

Add the vegetable oil and vanilla extract to the mixture, whisking until fully incorporated.

In a separate bowl, sift together the flour, baking powder, baking soda, and salt. Sifting helps to aerate the flour and remove any lumps.

Gradually add the dry ingredients to the wet ingredients, folding gently with a spatula until just combined. Be careful not to overmix, as this can result in a dense cake.

Grease and flour a 9-inch round cake pan to prevent sticking. You can also line the bottom with parchment paper for easier removal.

Pour the batter into the prepared cake pan, smoothing the top with a spatula.

Bake in the preheated oven for 30-35 minutes, or until a toothpick inserted into the center comes out clean. This indicates that the cake is fully baked.

Once baked, remove the cake from the oven and allow it to cool in the pan for 10 minutes. Then, transfer it to a cooling rack to cool completely.

In a small bowl, whisk together the powdered sugar, milk, and vanilla extract until smooth. Adjust the milk as needed to achieve your desired consistency.

Once the cake is completely cool, drizzle the glaze over the top. Allow it to set before slicing.