Preheat the oven to 350F/176C. Line 3, 8-inch cake pans with parchment paper; set aside.
In a large bowl, cream together the sugar and softened butter on high speed for 3 to 4 minutes until light and fluffy. Add the eggs, vanilla and lavender and continue mixing until well combined, another 2 to 3 minutes. Pour in the milk and add a few drops of purple gel food coloring, if desired.
In a separate bowl, combine the dry ingredients: flour, baking powder and salt. Using a fine mesh strainer/sifter, sift the dry ingredients into the cake batter. Whisk after each addition just until combined. Divide the prepared cake batter evenly between the prepared cake pans.
Bake in the preheated oven for 30 to 32 minutes, until the center is done and a toothpick inserted into the center comes out clean. Remove the cake layers out of the pans and place on to wire rack to cool completely.
Prepare the Italian meringue buttercream. Place the egg whites in a stand mixer bowl and whisk on high speed just until soft peaks form, about 2 minutes. Meanwhile, prepare the sugar syrup. Place the sugar and water into a small saucepan and cook over medium heat until the syrup reaches 240F/115C - do not stir the syrup!! Once the syrup has reached the proper temperature, set your stand mixer to medium speed and add the hot syrup in a slow stream into the egg whites. Continue whisking on high speed for 5 to 7 minutes until stiff and glossy peaks form.
Begin adding the butter. Add a few tablespoons at at time and scrape down sides of bowl often. Once all the butter is added, add the vanilla extract (and optional lavender extract) and continue whisking on high speed for 5 to 7 minutes until the buttercream comes together nicely.
To create the ombre frosting effect: divide the buttercream evenly between three mixing bowls. Leave one bowl plain white and into the other two bowls, add increasing amounts of purple food coloring. Mix in the food color thoroughly, then frost the cake is steps. Use the darkest buttercream first, then the lighter one, then the plain white buttercream.
To assemble the cake: spread approximately 1/4 cup peach preserves onto each cake layer and then top with frosting; repeat with second cake layer. Frost the outside of cake as desired. Keep the cake covered and refrigerated when not serving; remove it 1 hour prior to serving to allow the cake to soften.