Preheat the oven to 375°. Line a large baking sheet with parchment paper. In a food processor, pulse the 2 1/4 cups of flour with the granulated sugar, baking powder, lemon zest, salt and 2 teaspoons of the poppy seeds. Add the butter and pulse until it resembles coarse meal. Add the 1 cup of heavy cream and pulse until evenly moistened.
Transfer the dough to a lightly floured surface, gather any crumbs and knead a couple of times until the dough just comes together. Using a lightly floured rolling pin, roll the dough into a 9-by-6-inch rectangle. Using a large knife, cut the dough into 8 scones. Transfer the scones to the prepared baking sheet and brush with heavy cream. Bake in the lower third of the oven for about 25 minutes, until firm and lightly golden. Let the scones cool.
In a medium bowl, whisk the confectioners’ sugar with the lemon juice and the remaining 1 teaspoon of poppy seeds. Brush the scones with the glaze and let stand until set, about 15 minutes.