Preheat oven 350 degrees. Grease 2 8" springform pans.
Prepare flax egg by whisking together ground flax and warm water. Set aside to gel.
Add dry ingredients to bowl of a standing mixer fitted with the paddle attachment. Turn on standing mixer to combine ingredients.
Add rose, soy milk, olive oil, applesauce, vanilla and food colouring to a seperate bowl. Whisk to combine.
Pour wet over dry, including the flax egg. Mix to combine.
Use a spatula to scrape up any dry parts from the bottom of the bowl. Scrape down sides and mix again.
Pour batter evenly into prepared pans.
Place pans onto a cookie sheet.
Bake for 35-37 minutes until a toothpick comes out clean from the centre of the cakes.
Allow the cakes to cool in the pans for 10 minutes before gently removing them. Place the cakes onto a wire rack to cool completely.
Add softened butter to a clean bowl. Beat butter until smooth. Add icing sugar 1/2 cup at a time. Add milk, vanilla, food colouring and salt and beat until light and fluffy.
Place one of the cakes onto serving plate.
Spread 1/3 of the frosting onto the bottom cake. If you are using jam, spread that evenly on top of the icing. Place the second cake on top. Gently press it down.
Finish icing the cake.