Preheat the oven to 350 degrees.
Cut the 1/4 cup butter into 4 pieces and place in the 9 inch cake pan. Place pan in oven and let butter melt 2-3 minutes. Use a pastry brush and brush the melted butter over the sides and bottom of the pan.
Sprinkle the brown sugar top of the butter. Layer the lemon slices on top of the brown sugar, making an outer circle and an inner circle, and overlapping the lemons.
In a medium bowl combine the flour, salt, baking powder, baking soda, crystallized ginger, and cardamom. Whisk until combined.
In a large bowl cream together the butter, sugar, and lemon zest. Mix until light and fluffy.
Add in the eggs and vanilla bean paste and mix well.
Add half of the flour mixture to the butter mixture and mix until just combined. Pour in the milk and slowly mix until well combined. Add the remaining flour mixture and mix until just combined.
Pour the batter carefully over top of the lemon slices in the pan. Bake for 45 minutes or until a toothpick inserted into the center comes out clean.
Let cool for 10-15 minutes then run a knife around the edge of the cake.
Place a platter or serving plate on top of the cake pan and quickly flip the cake onto the plate.
Allow to cool completely before cutting and serving.