Position a rack in the center of the oven and preheat to 375º. Grease a 9" round springform pan.
Heat the milk in a small saucepan until small bubbles form around the edges and it gives off some steam. Stir in the poppy seeds and set aside to steep while you get on with the rest of the cake. (This can be done up to 2 hours in advance.) The seeds should absorb all of the milk. If they seem dry, add a bit more milk. If they are overly wet, pour off any unabsorbed milk before adding to the batter.
Sift together the flour, baking powder, soda and salt in a medium bowl.
Combine the butter and sugar in the bowl of a kitchen aid fitted with the paddle attachment. Grate the zests right in, and beat on medium speed until light and fluffy, about 5 minutes. Beat in the vanilla, then the egg yolks, one at a time, until well combined.
With the mixer on low, add the soaked poppy seeds to the butter mixture, stirring to combine. Add half of the flour mixture, all of the buttermilk, and the other half of the flour mixture, stirring to combine after each addition. Remove the bowl from the mixer and fold the batter by hand a few times, scraping the sides, bottom and paddle, to make sure it is homogeneous.
In a clean, large bowl (or the now-empty bowl you used for the dries), whip the egg whites with a whisk until they hold soft peaks. Stir 1/4 of the egg whites into the batter to lighten it, then fold in the rest of the whites with a rubber spatula until just combined and no streaks remain.
Pour the batter into the prepared pan and smooth gently. Bake until the cake is a dark, burnished brown on top, begins to pull away from the sides of the pan, and springs back to the touch, about 45 minutes, rotating once or twice. Remove from the oven.
When the cake is almost finished baking, make the glaze:
Combine the tangerine juice, lemon juice and sugar in a small saucepan. Cook over medium heat, swirling occasionally, until thickened and syrupy, about 5 minutes. The liquid should reduce by about half.
Brush the warm glaze over the top of the warm cake until it has absorbed it all, and let cool completely before slicing, serving and devouring.