Place a few inches of water in a medium saucepan and set a medium heatproof bowl on top of the pan (the water should not touch the bottom of the bowl.) Bring the water to a boil, then reduce the heat slightly to keep it simmering.
Meanwhile fill a large, shallow bowl or pie plate with a couple of inches of cold water and ice cubes, and set aside.
Add the egg yolks, the granulated sugar and the Moscato to the heatproof bowl over the boiling water.
Use a wire whisk or a hand mixer to constantly whisk the ingredients, until the mixture has turned pale yellow and is smooth: it will take about 7-10 minutes and the mixture will reach a temperature of 140°-150° F. Remove the bowl from the saucepan.
Gently stir the chocolate pieces into the sabayon until the chocolate has melted and the sabayon is smooth. Set the bowl of sabayon onto the large bowl filled with ice water to begin to chill it.
Stir the sabayon gently until it's cool. The volume will decrease and it will become thick and rich.
Fold in the whipped cream.
Cover with plastic wrap and chill the sabayon in the fridge for 30 minutes or longer.
Divide the sabayon between 5 serving dishes. Sprinkle the tops of each sabayon with crushed shortbread cookies. Garnish each dish with sliced strawberries and serve immediately.