Making the cake:

1. Preheat oven to 350°F /180°C.
2. Butter and flour 10-cup (26cm) bundt pan (see notes below) or spray with a baking spray containing flour. Refrigerate while preparing the batter.
3. In a large bowl (or the bowl of a stand mixer with the paddle attachment), cream the soft butter and gradually add sugar.
4. Beat for 3 minutes until it is creamy and light.
5. Add lemon zest, vanilla extract, and mix well.
6. Add eggs, one at a time, beating well after each addition.
7. Add sifted flour with salt and baking powder in 3 parts, alternating with the milk in 2 parts. That means you begin and end with flour.
8. Beat at low speed until it is well mixed but don’t overbeat.
9. Add poppy seeds and mix with a spatula, making sure you scrape the bottom of the bowl and the batter is uniform.
10. Pour batter into the prepared bundt pan (that is cold from the refrigerator) and even it out. 
11. Lift the pan and bang it lightly against the counter so that any air bubbles rise to the top and you can pop them. This will prevent (as much as you can) the batter from baking with holes inside.
12. Bake for 1 hour or so, until a cake tester or toothpick inserted in the center comes out clean. It might take 5-10 more minutes or sometimes less, depending on the pan you use and the material it is made of.
13. Remove from the oven and place on a wire rack.
14. Prepare the syrup mixture. Brush the top with half of the syrup. Please read step 17, below.
15. Let cool 15-20 minutes, making sure the syrup didn’t stick to the sides.  Grab the pan with both hands (and a kitchen towel) and shake it a little, up and down and left to right. You will feel that it loosens. At some point, you will be certain that the whole cake is loose and you will re able to remove it whole.
16. If some parts are sticking, carefully use a smooth-bladed knife to separate the cake from the sides and the center.
17. IMPORTANT: if you prefer to wait 15-20 minutes while the cake cools on a wire rack after you remove it from the oven, do so. Remove it first and then add the syrup. The cake will still be hot enough to absorb it but not as much as if you do it while pipping hot. It will leave a thin layer of sugar. BUT, you will remove the cake more easily from the pan. 
18. Brush the rest of the syrup on the rest of the cake (the bottom that will become the top when you serve it) right after you remove it from the pan, before flipping it over. You will now have the whole cake brushed with syrup. 
19. Put the cake on a cooling rack and let cool completely. 
20. Place the cooled cake in the cooling rack over a large piece of parchment paper. Pour the glaze over and let it run down the sides. 
21. If it’s too thin add a second layer of glaze, scooping it from the paper or making a new batch.

Making the syrup:

1. Mix the sugar with the room temperature juice right before you brush it. See Notes, below.
2. The sugar will not dissolve completely and that is fine.

Making the glaze:

1. Mix the powdered sugar with half the juice and mix.
2. Add the rest by half teaspoons until you have a smooth mixture as thick or as thin as you like. You might not use the whole amount of liquid.