Heat oven to 350°F. Make sure your oven rack is in the middle of the oven. Prepare loaf pan with butter or cake release and a piece of parchment paper that hangs over the long sides of the pan. You can use clips to hold the paper down remember to remove them before baking the cake.
Melt the butter and let it cool.
In a large bowl whisk together the sour cream and vanilla until smooth. You do not want any lumps.
In a separate bowl, whisk together the sugar and eggs until well mixed then add that to the sour cream and whisk those together well.
Clean out the bowl you used for the sugar and eggs and sift together the flour, baking powder and salt.
Alternate adding in the flour and melted butter to the sour cream mixture and mix until you don't see any more streaks of flour. There will be some small lumps of flour and that's OK. You just don't want large lumps of flour. This is why I prefer to sift the flour over because it helps make it so there's no large lumps of flour.
Scoop about a little less than half of the batter into the prepared pan, then scatter half of the diced plums over the batter. Top with the remaining batter.
Mix together the brown sugar, cinnamon and cardamom and sprinkle half of it over the top of the cake.
Next, using a decorating piping bag or a plastic baggie with a corner cut put the soft butter in the bag, squeeze to the end of the piping bag or baggie, cut open so there's a small opening in the piping bag or corner or the baggie, and pipe a line down the middle of the cake. Scatter the remaining plums all over the top of the cake on either sides of the piped butter line, then sprinkle the remaining brown sugar over the top of the cake.
Place the cake in the oven and bake for 45 to 60 minutes until the cake is golden brown and a skewer stuck into the middle comes out mostly clean. A few crumbs is OK.
Let the cake cool in the pan for 15 minutes then using the overhanging parchment paper, carefully lift it onto a wire cooling rack to cool completely before serving.
You can serve the cake warm or room temperature goes great with a scoop of vanilla ice cream.