Make the lavender whipped cream. Heat the heavy cream in a small pot over low heat until it starts to steam but doesn't boil. Add the lavender and stir to combine. Remove the cream from heat and cool completely. Chill the cream in the fridge until cold, preferably overnight. Strain the lavender and whip the heavy cream until stiff peaks form. Add the powdered sugar and vanilla, whipping until combined. Keep in the fridge until ready to serve.
Preheat oven to 350 degrees F.
Prepare the cake. Add 2 tablespoon melted butter in a 10-inch cast iron pan or cake pan. Sprinkle ¼ cup sugar in an even layer on the butter. Slice the plums into ¼ inch thick wedges and arrange them in the pan slightly overlapped.
Combine the ¾ cup softened butter with the remaining 1 ¼ cup sugar in the bowl of a stand mixer. Cream together the butter and sugar until light and fluffy, about 3 minutes. Add the eggs one at a time, fully incorporating one egg before adding the next. Add the buttermilk and vanilla and mix until combined.
Combine the dry ingredients together including the flour, cornmeal, baking powder, baking soda, and salt. Add the dry ingredients to the batter, stirring just until combined. Stir in the shredded cheese, mixing just until combined.
Pour the cake batter on top of the plums in an even layer. Bake the cake for 45-50 minutes or until a toothpick inserted in the center comes out clean. Remove from the oven and let cool for 15 minutes.
Place a plate on top of the cake and carefully invert the cake. Serve the cake warm or at room temperature with the lavender whipped cream.