Butter a 9” cake pan, line with a round of parchment, and butter the parchment.
Heat the brown sugar, 42 grams butter, and pinch salt in a medium saucepan, stirring constantly, until the butter is melted and the sugar is dissolved. Pour caramel into prepare cake pan, and arrange the apricot halves cut side down in the pan.
In a stand mixer with paddle attachment, cream 113 grams butter, white sugar, and lemon zest until fluffy. Add eggs one at a time, beating well after each addition.
In another bowl, whisk cake flour, cornmeal, baking soda, and salt.
Add a third of the flour mix to the butter and egg mixture, then add half of the buttermilk and vanilla, alternating until flour and butter milk is all added (ending on flour), mixing until just combined after each addition. Scrape bowl between additions.
Pour batter over apricots and use an offset spatula to smooth the top.
Give the cake pan a few taps on the counter to encourage the cake batter to settle between the apricots.
Bake at 350 until golden, puffed, and a toothpick inserted into the center of cake comes out clean - 40-50 minutes.
Allow to cool in cake pan, then turn out onto a plate.