Set oven temp to 375℉
Butter cake pan and dust lightly with flour.
Place small, heavy bottom skillet on a burner and set burner to setting 4.
Add brown sugar and 3 tbsps. of the butter and cook until the butter is melted and the brown sugar is dissolved and all is bubbly and cohesive, about 5 minutes.
Toss plums with lemon and ½ tsp of kosher salt, then place them face down in the prepared cake pan.
Pour brown sugar mixture evenly over plums.
Place remaining butter and the sugar in kitchen aid bowl. Start slow and gently increase speed to setting 3. Mix for 2 minutes.
Add almond extract and brandy. Continue mixing for 2 additional minutes.
Increase to setting 4, mix for 2 minutes and then add eggs one at a time mixing for 2 minutes between each addition.
Add sour cream and mix for 2 minutes.
Quickly combine flour, ½ tsp of kosher salt, ground anise, ground cinnamon and baking powder in a separate bowl.
Reduce mixer speed to setting 2 and add flour mixture to the Kitchen Aid mixer, add ½ at a time in two separate additions.
Mix for 2 minutes, pause, scrape sides with rubber spatula, resume and mix for 1 minute more.
Using rubber spatula, gently spoon batter over plums and distributing evenly. Smooth the top and pop the cake in the oven.
Bake the cake in the center rack for 45 minutes.
Finished cake should look fluffy, golden and spring back when gently pressed. Remove it from the oven and let it rest for 5 minutes.
Turn cake out onto a cake plate. Let the cake sit turned upside down for 10 minutes before removing cake tin. Cool completely before serving.
Serve as is or garnish as you like with powdered sugar, spun sugar, softly whipped cream, demerara sugar, ice cream etc.