In a large mixing bowl, cream butter and sugar together until light and fluffy. This should take about 3-4 minutes.
Beat in eggs one at a time, making sure each one is fully incorporated before adding the next.
Add vanilla extract and buttermilk, and mix well.
In a separate bowl, whisk together flour, baking powder, baking soda, and salt. Gradually add the dry ingredients to the butter mixture, mixing until just combined.
On a floured surface shape the dough into a disk, cover with plastic wrap and refrigerate for at least 1 hour or overnight.
When ready to bake, preheat the oven to 350°F. Line baking sheets with parchment paper or silpat mats.
Working on a floured surface, roll the dough out to a ¼ inch thickness. Cut dough into desired shapes Place the cut out dough on the prepared pans, at least 2 inches apart.
Bake 10-12 minutes, or until the edges are just starting to turn golden. The centers should still be soft.
Allow the tea cakes to cool on the baking sheets for a few minutes before transferring them to a wire rack to cool completely.