1preheat the oven to 325°. Line the bottom of an 8 inch square baking dish with parchment paper, and butter the sides of the dish.
2combine the butter and granulated sugar in a bowl Of a stand mixer fitted with a paddle attachment and beat until light and creamy.mix in the vanilla. Beat in eggs one at a time, scraping down the sides of the bowl after each addition.
3sift together the flour, baking powder, and fine sea salt. Add half of the flour mixture to the batter and beat until mixed, then add the milk and beat until combined. Add the remaining flour mixture, and mix until just combined. Pour the batter into the prepared dish and bake for about an hour, until the top of the cake is Golden Brown and a cake tester comes out clean.
4brush the top of the warm cake with vanilla simple syrup and sprinkle with vanilla sugar if desired. Add a hint of grinder sea salt. Let the cake cool for at least 30 minutes before cutting. Serve warm or at room temperature. The cake will keep, covered, at room temperature for up to two days.
5vanilla simple syrup:
1/2 cup sugar
1 teaspoon pure vanilla extract
pinch the fine sea salt
1 cup water
mix the vanilla, sugar, salt and water in a small pan over low heat and simmer, stirring occasionally, for 4 to 5 minutes until the sugar is dissolved. Use At once or refrigerate in airtight container for up to two days.