Heat heavy cream in a small saucepan over medium heat until steam begins to rise. Add semi-sweet chocolate chips, brown sugar and cinnamon; whisk until the chocolate has melted and the brown sugar has dissolved.
Remove from heat and whisk in vanilla extract.
Pour into a heat-proof container and allow to cool before covering and refrigerating until chilled, about 2 hours.
Once the mixture has chilled, pour it into a large bowl {or the bowl of a stand mixer} and beat until the it is light and fluffy.
Carefully fold in the yogurt, a bit at a time until the mixture is uniform and smooth.
Spoon into individual serving cups. Keep refrigerated until ready to serve. Top with chocolate shavings before serving if desired.