Preheat oven to 350°F (325°F for dark pans).
Melt butter in a 10-inch round cake pan or cast-iron skillet. Sprinkle brown sugar evenly over the butter. Lay out the fruit; fruit should be one layer thick, covering the bottom of the pan. If using herbs, sprinkle on top of the fruit. Place pan in the refrigerator while making the batter so the placement of the fruit can solidify.
Whisk the cake flour, baking powder, baking soda, and salt together. Set aside.
Using a mixer, beat butter on high until creamy, about 1 minute. Add sugar and cream together. Beat egg until well combined, and then add vanilla and sour cream. Pour in dry ingredients, turn mixer to low, and slowly add milk until combined, but don’t overmix.
Remove the pan with the fruit from the refrigerator and pour the batter over the fruit, using care not to disturb fruit. Bake for 45–50 minutes or until a toothpick inserted in the center comes out clean. Remove from the oven. Run a knife around the edge of the pan and turn the pan over onto a platter quickly. Leave the pan on top of the cake for about 3 minutes, then carefully lift it. If any pieces of fruit are stuck to the cake pan, gently scrape them up with a knife and replace them on the cake. Let the cake cool before serving.