Set the butter in a large non-stick frying pan. Cook on medium low, as the butter melts, then begins sputtering, then foams as it browns on the bottom - the process will take about 7 minutes or so. If you are using a vanilla bean, slice it open and add it and the scrapings to the melted butter. Stir it as it browns, scraping up the edges with a rubber spatula for even browning. Once the butter goes quiet and is close to stopping foaming, transfer 226g of it to a large bowl, scraping up the bits off the pan. Discard vanilla pod, if using.
Preheat the oven to 350 F. Line an 8 or 9” square pan with parchment paper or grease and flour it.
Sprinkle the sea salt into the butter and pour in the vanilla and whisk. Add the brown sugar and whisk for a full minute, the sugar should melt somewhat.
Add one egg, then whisk for a full 60 seconds. Add another egg and whisk again - at this point you’ll see the mixture turn thick and shiny, a sign the emulsion is happening. Add the last egg and whisk for another 60 seconds.
Sift in the flour, baking powder, baking soda and whisk until it’s half mixed, then add the sour cream and whisk fully. Stop when there are no flour bits visible.
Pour into the prepared pan and sprinkle generously with granulated sugar. Bake until a cake tester comes out clean, about 35-45 minutes.