Heat the oven to 350°F (175°C). Butter a 9-inch round cake pan and line the bottom with a circle of parchment.
Melt the butter in a heavy-bottomed saucepan over medium heat. Keep it moving once it starts foaming. After 5-7 minutes, the foam will subside and the milk solids on the bottom will turn deep amber and smell like toasted hazelnuts. Pull it off the heat immediately and pour it -- brown bits and all -- into a heatproof bowl. Let it cool to barely-warm.
Whisk the flour, cornmeal, granulated sugar, baking powder, and salt together in a large bowl.
Whisk the eggs, milk, lemon zest, and vanilla into the cooled brown butter.
Pour the wet into the dry and fold with a spatula until just combined. The batter should look like loose porridge with no streaks of flour. Stop folding.
Scrape into the prepared pan and smooth the top. Sprinkle the turbinado over the surface if you want a crackly top.
Bake for 32-38 minutes. The cake is done when a skewer comes out with a few moist crumbs and the edges have pulled away from the pan. Cool in the pan for 15 minutes, then turn out onto a rack.
Source: Adapted from our own kitchen over many cornmeal cakes that came out wrong before this one came out right.
Cornmeal cake is the dessert equivalent of a workhorse pickup truck: unfussy, dependable, and quietly capable of carrying you through nearly any meal. We make this version when peaches show up at the market in July and when blood oranges arrive in February, and it has never disappointed us in either season.