Preheat your oven to 350 degrees Fahrenheit and grease and flour a 9-inch bundt pan.
In the bowl of your stand mixer, or in a mixing bowl with a hand mixer, add the eggs, sugar and oil. Mix on medium speed until well mixed. Scrape down the sides of the bowl and mix on medium high speed for a few minutes until pale in colour. Add the lemon zest and juice and vanilla and mix.
Add the flour, baking powder, salt and poppy seeds to the bowl with the egg mixture.
With the mixer running, add the milk in a steady stream as the flour mixture and the egg mixture combine. After all the milk is added, mix well just until combined (about 30 seconds on medium speed), scraping down the sides of the bowl to make sure everything is incorporated.
Pour the batter into the prepared bundt pan and smooth out the top. Bake for about 60-65 minutes at 350 degrees Fahrenheit, or until a toothpick inserted into the middle of the cake comes out clean.
Cool in the pan for at least 15 minutes before inverting the pan (place an upside down cooling rack on top of the pan before flipping it over) to cool completely.
Whisk together the glaze ingredients (you may have to add an extra teaspoon of lemon juice to achieve the desired consistency) and drizzle the glaze over the cake when it's completely cooled.
Sprinkle the reserved lemon zest over the top of the cake as well as a few extra poppy seeds (if desired).
Slice and serve.