Whisk the egg yolks, sugar, half & half, vanilla, and two pinches of salt together in a medium sauce pot over medium heat. Heat until the edges of the pot start to bubble, whisking continuously, then remove from the heat.
Pour the mixture through a sieve into a bowl to remove any particles. Cover and chill for at least 4 hours.
Once the mixture has chilled, pour it into an ice cream maker and churn for 20+ minutes to the desired consistency. Meanwhile, shave the chocolate bar with a vegetable peeler, so the pieces are very thin.
Scoop a quarter of the gelato into a plastic container. Drizzle some of the caramel and chocolate shavings over the gelato, then repeat with the remaining gelato, caramel, and chocolate shavings, filling the container in layers. Cover and place in the freezer until firm. Scoop into small cups and serve!