Turn the oven on to 400 degrees to preheat. Line a baking sheet with parchment paper and position your oven rack in the center of the oven.
In a large bowl, stir together the flour, poppy seeds, baking powder, baking soda, salt, cornstarch, and sugar. Add the lemon zest and stir well.
Take the butter and cut it into slices, and then cut the slices into chunks. Work quickly to keep the butter as cold as possible. Use a pastry blender to cut the butter into the dry ingredients. Add the cold cream and stir gently, just until the dough begins to stick together. Do not over mix.
Press the dough into a ball and then gently turn it out onto a lightly floured surface. Working gently, press the ball with your hands to make a disc that is about 8 or 9 inches in diameter. Cut the disc into 8 or 10 wedges. Gently, use a spatula to transfer the scone wedges to your prepared baking sheet, spacing them about two inches apart. Brush the scones lightly with 1 tablespoon of milk.
Slide the scones into the fridge to chill for about 15 to 20 minutes.
Put the scones into the oven and bake them for 12 to 15 minutes. They should be a light golden brown color. If they are not, return them to the oven and check them again in 2 minutes.
When the scones are fully baked, remove them from the oven and transfer them to a wire rack to cool.
While the scones are in the oven, you can create the lemon glaze. To a small bowl, add the lemon juice, milk (or heavy cream), and powdered sugar. Use a wire whisk to blend these together. This mixture should make a smooth glaze. You do not want it to be too thick or too thin. If your mixture is too runny, add a bit more powdered sugar a little at a time. If it is too gloppy, add another small spoonful of liquid.
When the scones are cool, take the wire rack on which the scones have cooled and place it on the baking sheet that you used previously for baking. Drizzle the glaze over the scones and allow the extra glaze to drip off of the scones onto the baking sheet.
Use the extra poppy seeds and sprinkle them over the tops of the scones. Wait about 5 to 10 minutes to allow the glaze to set before serving. Store leftovers in a container with a loose-fitting lid for up to three days.