Sprinkle the gelatin over the milk and allow to sit to soften the gelatin.
Heat the half-and-half in a medium saucepan over medium-low heat until it comes to a simmer.
Whisk in the sugar, chocolate chips and vanilla extract. Bring to a simmer and cook, stirring frequently, until the chocolate has melted. Add the milk and gelatin mixture and whisk until the gelatin has entirely dissolved. Bring the entire mixture to a simmer.
Ladle the mixture into six 6-ounce custard cups or ramekins (or serving dishes of your choice) and refrigerate until set, about 6 hours.
To serve, top the panna cottas with whipped cream and chocolate shavings.