Preheat oven to 350˚F. In a cast iron skillet, melt 3 tablespoons of the butter over medium heat. Use a pastry brush to coat the sides of the skillet. Sprinkle 1/4 cup of the sugar evenly over the bottom of the skillet, and continue to cook until the sugar turns golden brown and begins to bubble, about 3 minutes. Starting at the outer edge of the skillet working towards the center, arrange the peaches in the skillet, slightly overlapping to fill the skillet. Reduce the heat to low, and cook 10-12 minutes more, until the peaches begin to soften and the juices are bubbling. Remove from heat.
In a medium bowl, whisk together the cornmeal, flour, baking powder, lavender, and salt. Set aside.
in a large bowl with a mixer on high speed, beat the last stick of butter and 3/4 cup of sugar until pale and fluffy, about 3 minutes. Reduce speed to medium. Add the eggs one at a time, beating well after each egg and scraping down the sides of the bowl. Beat in the vanilla extract and heavy cream. Reduce speed to low, and add half of the cornmeal mixture and beat until incorporated. Beat in the remaining cornmeal mixture.
Drop large spoonfuls of the cornmeal batter over the peaches in the skillet, and with a spatula, gently spread it in an even layer. Bake 20-22 minute, until golden brown and a tester inserted into the center comes out clean. Allow to cool on a wire rack for 10 minutes. Run a sharp knife around the edge of the cake. Quickly invert the skillet onto a cutting board or serving dish. Firmly tap the bottom of the skillet to release the peaches, and carefully remove the skillet. If needed, reposition the peaches on top of cake. Allow to cool another 10 minutes before serving.