Preheat the oven to 350 degrees. Lightly grease an 8-by-8-inch square cake pan with nonstick cooking spray. Line the bottom with parchment paper, leaving a two-inch overhang on the sides (to make it easier to remove the cake after baking), and grease the parchment.
In a medium bowl, whisk together the flour, cornmeal, baking powder, baking soda, and salt. Set aside.
In a large bowl, beat the butter with an electric hand mixer or in a stand mixer fitted with the paddle attachment until smooth. Add the sugar and honey and cream the mixture until light and fluffy, 2 to 3 minutes. Scrape down the bowl with a rubber spatula.
Beat in the eggs one at a time, scraping the bowl after each addition, then beat in the vanilla.
Add half of the dry ingredients to the egg mixture and beat just until combined. Carefully beat in the milk and sour cream, then beat in the rest of the dry ingredients just until the batter is smooth.
Transfer the batter into the prepared pan and smooth the surface with an offset spatula. Bake the cake for 30 to 35 minutes, rotating the pan halfway through, until golden brown and a toothpick inserted in the center comes out clean.
Let the cake cool for 15 minutes, then gently run a knife around the edges to loosen. Using the parchment sling to assist, transfer the cake to a cooling rack.
Make the glaze: Thoroughly mash the blueberries in a medium bowl with the back of a large spoon. Let the berries macerate for a minute or two. Add balsamic vinegar, powdered sugar, and a few pinches of salt to the bowl and whisk until smooth. The consistency of the glaze should be pourable but not overly runny — if needed, add more powdered sugar, a tablespoon at a time.
Set out a rimmed baking sheet. When the cake is completely cool, set the cooling rack (with the cake on it) over the parchment or baking sheet. Pour the glaze over the cake, spreading it to the edges and letting it run down the sides. Allow the glaze to set completely before slicing and serving.