Adjust the oven rack to the center position and preheat the oven to 350 degrees F. Butter and flour a standard 12-cup Bundt pan or spray with Baking Spray with flour. In a large bowl, sift together the flour, baking soda, baking powder, and cornstarch, whisk in the poppy seeds, and set it aside.
In the stand mixer bowl, beat the butter and sugar on medium speed until light and fluffy, about 5 minutes. Add the eggs, one at a time, beating well after each egg and scraping down the sides of the bowl. In a two-cup liquid measuring cup, combine ¼ cup of the lemon juice, zest, vanilla, and buttermilk. With the mixer on low speed, alternately add the flour mixture and buttermilk mixture in thirds, beginning and ending with the flour. Scrape down the sides of the bowl with a rubber spatula and give a quick mix to be sure the batter is well incorporated.
Pour the lemon batter into the prepared bundt and smooth the surface. Bake for 40 to 50 minutes, or until a cake tester or skewer inserted in the center comes out clean and the edges start to pull away from the sides of the pan. Let cool in the pan for 10 minutes, then invert onto a rack and cool completely.
Meanwhile, make the Vanilla Glaze: In a medium bowl, whisk together the powdered sugar, 3 tablespoons heavy cream, and both vanilla until smooth, adding more heavy cream as needed, 1 teaspoon at a time, until the glaze is pourable. Spoon the glaze over the Lemon Poppy Seed Bundt Cake and sprinkle poppy seeds over the ice if desired; allow the glaze to set for 20 minutes before slicing.