Preheat Oven: Preheat your oven to 350°F (175°C). Grease and flour two 8-inch round cake pans to prevent the cake from sticking.
Mix Dry Ingredients: In a large bowl, whisk together 1 1/2 cups of all-purpose flour, 1 1/2 cups of granulated sugar, 1/4 cup of poppy seeds, 1 teaspoon of baking powder, and 1/2 teaspoon of salt until well combined.
Combine Wet Ingredients: In another bowl, mix 1 cup of milk, 1/2 cup of melted butter, 1/4 cup of lemon juice, 2 tablespoons of lemon zest, 1 teaspoon of vanilla extract, and 4 large eggs until they are thoroughly blended.
Combine Wet and Dry Ingredients: Gradually add the wet ingredients to the dry ingredients, stirring gently until just combined. Be careful not to overmix.
Divide and Bake: Divide the batter evenly between the prepared cake pans. Spread it evenly across the bottoms. Bake in the preheated oven for 25-30 minutes or until a toothpick inserted into the center comes out clean.
Cool Cakes: Once baked, let the cakes cool in the pans for about 10 minutes, then transfer them to a wire rack to cool completely.
Prepare Lemon Pudding: Meanwhile, in a separate bowl, prepare the lemon pudding by mixing 1 cup of lemon pudding mix with 2 cups of milk, stirring until well combined. Chill until set according to package instructions.
Make the Glaze: In a small bowl, whisk together 1 cup of powdered sugar and 2 tablespoons of lemon juice until smooth to create the glaze.
Make the Frosting: In a large bowl, beat 1 cup of softened unsalted butter until creamy. Gradually add 1 1/4 cups of powdered sugar, 2 tablespoons of lemon juice, 1 tablespoon of lemon zest, and 1 teaspoon of vanilla extract, beating until smooth and fluffy.
Assemble the Cake: Once the cakes are completely cool, spread a layer of lemon pudding on top of one cake layer. Gently place the second cake layer on top.
Frost the Cake: Use the lemon frosting to cover the top and sides of the layered cake, smoothing it out with a spatula to achieve a nice finish.
Drizzle the Glaze: Finally, drizzle the glaze over the frosted cake to add a final touch of sweetness and tanginess.