In a frying pan over a medium heat, toast the almonds until golden, stirring frequently. Then allow to cool. In a food processor or a blender, blend almonds until finely ground. Set aside.
Line 2 large baking sheets with baking parchment or foil. Using 20-cm/8-inch round plate or cake tin as a guide, mark 2 circles on each baking sheet.
Preheat oven to 140°C (275°F / gas mark 1). In a large bowl, with the electric mixer on full speed, beat egg whites until soft peaks form. Gradually sprinkle in the sugar, 1tbsp at a time, beating well at each addition until whites stand in soft, glossy peaks.
In the meringue mixture, using a wire whisk or rubber spatula, carefully fold the ground, toasted almonds.
Spoon one quarter of the mixture inside each circle on baking parchment or foil; with palette knife, evenly spread meringue to cover entire circle.
Place baking sheets with meringue on two oven racks and bake for 30 mins. Switch baking sheets between racks so the meringue browns evenly: bake for 30 mins longer or until golden.
Cool meringues on baking sheets on wire racks for 10 mins. Using a fish slice, loosen the meringues from the baking sheets and transfer to the wire racks. Cool completely.
Hull and thinly slice 150g (5oz) strawberries. Prepare the chocolate butter cream (see cook's notes below).
Place 1 meringue layer on a serving platter and using a palette knife, spread with one third of the butter cream. Top with one third of the sliced strawberries. Make 2 more layers and top with the last meringue layer.
In a medium-sized bowl, whisk the double or whipping cream until stiff peaks form. Spoon about one third of the cream into a piping bag with large star tube and set aside.
Spread the remaining whipped cream on the top and side of the gateau. Decorate the top edge with the cream from the piping bag and use a four-pronged fork to make vertical line around the side of the cake.
Chill the dacquoise in the fridge for 4 hrs to soften the meringue layers slightly, making it easier to cut.
Cut 16 slices from the remaining strawberries and press into the cream on the side of the cake.
Top the cake with the remaining strawberries, hulled and cut in half.