Step 1Heat oven to 375 degrees.
Step 2In a large 10- to 12-inch skillet, preferably cast iron, melt the 3 tablespoons of butter over medium heat. Add the brown sugar and stir until dissolved, about 1 minute. Add three-fourths each of the cherries and blueberries to the skillet, along with the ginger, and stir gently so that they are evenly coated with the butter and sugar. Add the water, cover the pan, and cook until the cherries and berries have also released their juices, about 3 minutes. Uncover and cook down over medium heat, stirring occasionally, until the mixture is thick, sticky and jammy, about 5 minutes. Toss in the remaining halved cherries and blueberries and stir to combine. If you are baking the cake in the skillet, set the whole thing aside to cool. If you will be baking the cake in a springform pan, scrape the cherry and berry mixture into a 9-inch round pan (line the base with parchment paper, to about one-half inch up the sides of the pan). Take care that the mixture is evenly spread to the edges of the pan.
Step 3In a medium bowl, whisk together the flour, sugar, baking soda, baking powder, salt, cinnamon, nutmeg, allspice and cardamom. In a separate, large bowl stir together the buttermilk and the remaining one-half cup melted butter. Then, working in batches, sift the dry ingredients into the wet ingredients, mixing gently, until just smooth and combined.
Step 4Pour the cake batter into the pan, over the cherry and berry layer; gently smooth the batter to the edges of the pan using a knife. Bake the cake until dark golden and a toothpick inserted into the center comes out clean, about 40 minutes (a springform cake will require additional time). Allow it to cool for 10 minutes, and then run a knife around the edges of the cake to loosen it, and turn the cake over onto a large platter. (If using a springform, place a plate over the pan, flip the pan over, release the spring mold, and peel back the parchment.) The cake will be best on the day that it is made. Serve it slightly warm or at room temperature.