Preheat the oven to 350°F. Line a 9-inch loaf pan with parchment paper and set aside.
Cream together the butter and sugar on high speed until light and fluffy. Add the eggs one at a time, incorporating the first egg before adding the remaining ones.
Add the well-shaken buttermilk and vanilla bean paste and mix to combine.
In a separate medium bowl, whisk together the flour, baking powder, baking soda, and kosher salt. Slowly add the dry ingredients to the butter mixture, mixing only until everything is just combined. Don't over mix.
Pour the batter into the prepared loaf pan and bake until the cake is golden and a toothpick inserted in the center comes out clean, about 45-50 minutes, depending on your oven.
The Vanilla Bean Glaze
In a small saucepan, combine the sugar, butter, and water and bring to a boil over medium-high heat, whisking occasionally. Remove the pan from the heat and let the glaze cool slightly.
Whisk in the vanilla bean paste.
Let the cake cool in the pan for 10-15 minute and then transfer to a cooling rack set over a baking sheet. This is to help prevent a big mess and to catch excess glaze.
Brush the glaze over the cake. Brush the tops, the bottom, the sides - all over, up and down. Be gentle and repeat until all of the glaze is on the cake. If you have the will power, you can reserve a little of the glaze to drizzle before serving.
Top with a little flaky sea salt while the glaze is still a bit wet. This is optional, but oh so good.
Let the glaze set up just slightly, slice the cake, and enjoy!