Combine the remaining 1/4 cup brown sugar, cranberries, liqueur or juice, grated orange peel and crushed cardamom seeds in a medium saucepan. Mix well and place on high heat. Bring the mixture to a boil, stirring briskly. Cook for 1 minute, then immediately remove the pan from the heat, and allow to cool.
Spoon the cranberry mixture into the cake pan over the creamed butter and sugar and spread evenly with a metal spatula. Set the pan aside and prepare the cake batter.
Preheat the oven to 350 degrees. Sift together onto a sheet of wax paper, foil or plate the flour, baking powder, baking soda and salt. Set aside.
Combine the 1 stick of butter, sugar and vanilla extract in the reserved mixing bowl. Using the electric mixer on medium-high speed, cream until light and fluffy, about 3 minutes, scraping the bowl as needed with a rubber spatula. Beat in the eggs, scraping the bowl after each addition, then beat the batter about 1 minute longer.
Stir together the buttermilk or yogurt and orange juice and mix well. Add the flour mixture and buttermilk or yogurt mixture alternately to the bowl, beginning with the dry ingredients, stirring only briefly after each addition. Then, set the mixer on medium speed and beat for 30 seconds, scraping the bowl at least once.
Spoon the batter into the prepared cake pan, and spread evenly over the cranberries. Shake the pan a couple of times to settle the batter. Place on the middle shelf in the center of the oven and bake for 40 to 45 minutes, or until a knife or toothpick inserted in the center comes out clean but moist, and the cake pulls away from the pan.