Preheat your oven to 325°F (160°C) and grease a 9-inch round cake pan.
In a big bowl, beat the softened butter and sugar until fluffy. Add the eggs one by one, mixing well each time.
In another bowl, sift together the cake flour, baking powder, baking soda, and salt.
Slowly mix the dry ingredients into the wet ones, alternating with buttermilk and vanilla extract, until everything's combined.
Pour the batter into the prepared cake pan and bake for 45-50 minutes, or until a toothpick comes out clean from the center.
While the cake bakes, make the glaze. In a small saucepan, cook together the butter, sugar, water, and vanilla extract until the sugar dissolves and the mixture thickens.
Once the cake's done, let it cool in the pan for 5 minutes, then transfer it to a wire rack to cool completely.
When the cake's cool, drizzle the glaze over the top, letting it run down the sides.
Slice, serve, and enjoy your homemade version of Maggiano's Gigi's butter cake!