Preheat the oven to 350°F (175°C). Grease and flour an 8-inch round cake pan or line it with parchment paper.
In a medium bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt until well combined.
In a large bowl, beat the eggs and granulated sugar together using a hand mixer or whisk until the mixture is pale and slightly thickened, about 2-3 minutes.
Add the vegetable oil, plain yogurt, lemon zest, lemon juice, and vanilla extract to the egg mixture. Mix until fully incorporated.
Gradually add the dry ingredients to the wet ingredients, folding gently with a spatula until just combined. Do not overmix.
Pour the batter into the prepared cake pan and smooth the top with a spatula.
Bake in the preheated oven for 35-40 minutes or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and allow it to cool in the pan for 10 minutes. Then transfer the cake to a wire rack to cool completely.
While the cake cools, prepare the lemon glaze by whisking together the powdered sugar and lemon juice in a small bowl until smooth.
Once the cake is completely cool, drizzle the lemon glaze evenly over the top of the cake.
Allow the glaze to set for 10-15 minutes before slicing and serving.