Preheat oven to 350 F. Line bottom of 12x9 brownie pan with parchment paper. Spray with non stick spray.
Beat sugar and butter until soft and creamy.
Add vanilla extract and mix to combine. Add eggs, mixing well after each addition.
In a medium bowl, combine flours, baking powder, nutmeg, salt and lavender.
Add half of the dry ingredients and mix well until thoroughly incorporated. Add the rest of the dry ingredients and mix until thoroughly incorporated.
Using a rubber spatula, fold in the peaches and walnuts.
Transfer to prepared pan and spread batter in an even layer.
Bake for 20 - 25 minutes, until set. Cool for 20 minutes in pan. Flip over onto plate or wooden board. Carefully peel parchment paper off of bottom. Cool completely before slicing.