Place all the ingredients in a small bowl.
Quickly rub them between your fingers until sandy.
Cover and cool in the refrigerator.
Put the milk and the butter in a small saucepan with the lavender flowers: heat the pan over low heat until the butter melts down. Let the mixture cool down and filter it.
Preheat the oven to 180°C.
Separate the whites of the eggs from the yolks. In a medium bowl beat the egg whites until they resemble a fluffy cloud, then set aside.
Mix the yolks, the sugar, the salt and the coconut flour. Add the milk and butter mixture, the flour and the baking powder.
Beat until the batter is foamy and homogeneous, then gently stir in the egg whites. Fill the batter into the baking pan (24-cm-diameter), previously buttered.
Cut the apples into thin slices and place them over the batter surface.
Sprinkle the crumble over the apples and bake for about 40 minutes. Serve cold.