Preheat the oven to 425 degrees F. Line a baking sheet with parchment paper.
Slice the vanilla beans in half lengthwise and use the flat side of a paring knife to scrape out the seeds.
In a medium bowl, whisk together the flour, sugar, vanilla seeds, cardamom, baking powder, baking soda, and salt.
Add the cold butter pieces and, using your fingers or a pastry blender, work the butter into the dry ingredients until the mixture resembles coarse cornmeal with a few larger pieces scattered around.
Add the cream and vanilla to the bowl and use a spatula to mix the ingredients until they are just combined. The dough will look like it’s barely coming together. Kneed the dough in the bowl until it comes together. Divide the dough in half and flatten into two round discs, about 7 inches in diameter. Cut each disc into 6 pieces. Brush melted butter on top of each piece.
Bake for 10-12 minutes, until both the tops and bottoms are golden. Serve warm.