To make the cake, in the bowl of a stand mixer fitted with the paddle attachment, cream the butter, brown sugar, granulated sugar and vanilla extract on medium-high, until light and fluffy, about 3 to 4 minutes. Add the eggs one at a time, and mix on medium until each is fully incorporated before adding the next one. Use a spatula to scrape down the sides and bottom of the bowl. In a medium bowl, whisk together the flour, baking powder, cinnamon, allspice, ginger and salt. Add half the dry ingredient mixture to the wet ingredients and mix on low until almost incorporated, about 1 minute. Add the yogurt and mix on low. Finally, add the rest of the dry ingredient mixture, mixing on low until just combined.
