Preheat oven to 350 °F. Grease and line bottoms of 2 8-inch cake pans with parchment, then grease and flour again, tapping out excess.
Heat milk and butter until butter is melted. Stir in vanilla and cover to keep warm. Separate 3 whites (reserving yolks) and beat them in a bowl with 6 Tbsp of sugar until they hold a soft peak (whites curl when beaters are lifted) and set aside. In another bowl, whip reserved 3 yolks and remaining 2 whole eggs and beat with remaining 6 Tbsp of sugar until thick and pale in colour, about 8 minutes. Fold whipped whites into whole egg mixture.
Sift flours, baking powder and salt and add to whipped eggs in 3 additions, folding gently but quickly. Spoon about ¾ cup of batter into warm milk mixture and stir to blend. Add back to batter and fold in quickly but gently. Scrape batter into prepared pans and bake for about 20 minutes, until cake springs back readily when pressed. Run a knife around the edges of the cake to loosen and allow cake to cool for 15 minutes before tipping out to cool completely.
To assemble, whip cream with skim milk powder until a soft peak. Add sugar and vanilla and whip until medium peak. Hull and slice strawberries. Spread half of the cream over top of bottom cake layer and top with half of the strawberries. Lightly set second cake on top and top with remaining cream and berries.
To serve, slice a wedge of cake and dust plate generously with icing sugar.