Preheat oven to 350 degrees. Line a baking sheet with parchment and set aside.
To make the lavender sugar: Mix one cup sugar and one tablespoon dried lavender buds into a small food processor. Pulse until well combined and aromatic. Measure out what is needed for the recipe. Use the rest to add to lemonade for a tasty treat.
In an 8-inch cast iron skillet over medium heat, melt the 4 tablespoons of butter. Once melted add brown sugar and gently whisk over heat until well combined. Remove skillet from heat and arrange peach slices in a circular pattern on top of the sauce in the skillet. Set aside.
In a medium bowl combine the baking mix, instant vanilla pudding mix, baking powder, and salt. Lightly whisk to combine and set aside.
Cream together the 12 tablespoons of butter and the lavender sugar in the bowl of a stand mixer until light and fluffy. Next add the egg and vanilla and mix on low until just combined (If you want to replace the egg, use egg replacer of choice according to package directions, or use ¼ cup applesauce in place of the egg). Add honey and coconut milk yogurt mixing until combined.
Add half of the dry ingredients to the wet mixture and mix on low speed until combined, scraping the bowl. Then add half of the non-dairy creamer and mix until combined. Mix in the last half of the dry ingredients, then the last half of the non-dairy creamer. Mix until just incorporated.
Pour cake batter on top of peach mixture in the cast iron skillet. Place skillet on the prepared baking sheet in case of spilling and place the sheet in preheated oven. Bake for 45 minutes, or until a toothpick stuck in the middle comes out clean.
Remove from oven and allow to cool for 10 minutes. Run a knife around the edge of the cake to help release the cake and invert onto a cake plate. Allow to cool for another 5-10 minutes. Garnish with dried lavender buds and whipped cream.