Butter a 9-inch cake pan. Line the bottom with parchment paper and butter the paper.
In a medium bowl, whisk the flour with the cornmeal, granulated sugar, baking powder and salt. In another medium bowl, whisk the melted butter with the eggs, grapefruit zest and grapefruit juice. While whisking constantly, add the butter mixture to the flour mixture in a slow, steady stream. Whisk until well blended.
Scrape the batter into the prepared pan and bake for about 40 minutes, until golden and a cake tester inserted in the center comes out clean.
Transfer the cake to a rack to cool for 10 minutes.
Run a sharp paring knife around the edge of the cake, then invert it onto the rack. Peel off the parchment paper. Carefully flip the cake right side up and set the rack over a baking sheet.
Let cool until warm, about 30 minutes.
In a medium bowl, mix the confectioners’ sugar and poppy seeds. While whisking constantly, slowly drizzle in the grapefruit juice until a smooth, thick glaze forms.
Pour the glaze all over the top of the warm cake and spread evenly over the top and side. Let stand until set, about 30 minutes.