Preheat the oven to 350 degrees F. Grease and line two 9 inch cake pans with parchment paper.
Add the poppy seeds to a food processor and blend until it resembles wet sand and smells aromatic. Alternatively, you could use a blender or immersion blender. Set aside.
In the bowl of a stand mixer fitted with a paddle attachment, add the sugar and lemon zest. Rub them together with your fingers until it resembles wet sand and smells aromatic.
To the sugar, mix in the flour, baking powder, and salt.
Cut up the butter into small cubes and add to the dry ingredients. Mix on low speed until it resembles wet sand.
Add the oil, whole milk, yogurt, eggs, and vanilla, and mix until fully combined.
Pour ¼ of the batter into a separate small bowl, then fold in the poppy seeds until evenly distributed.
Use cookie scoops to alternate the two batters between each pan, adding an equal number of scoops to each. Use a knife to swirl the batters together, then gently shake the pans to encourage them to spread out into an even layer.
Bake the cakes for about 25-30 minutes or until the cakes start to pull away from the sides of the pans. Immediately turn the cakes out onto a wire rack to cool completely.
Once cool, wrap the cakes in plastic wrap and freeze until ready to decorate. (Frozen cake layers will be much easier to frost!)