Mix the buttermilk with the water and vanilla and set aside.
Mix the eggs and yolk together in a measuring pitcher and set it aside.
Whisk the flour, salt, baking powder, and baking soda together in bowl large enough to do this job thoroughly—whisking not only combines the ingredients, it fluffs up the flour so that it blends more easily into the batter which in turn prevents over mixing. Set this aside.
In the bowl of a stand mixer fitted with the paddle attachment, beat the sugar, butter, and ground coriander on medium high speed until pale and fluffy, about 3 minutes.
Very gradually pour the eggs into the bowl in a thin steady stream taking 1 to 1½ minutes in total.
On low speed, starting and ending with the flour mixture, add the flour in three additions, alternating with the buttermilk mixture in two additions. Scrape the bowl as necessary and mix only enough to incorporate each addition.
Scrape the batter into the prepared pan and spread it evenly.