Preheat the oven to 325 degrees Fahrenheit. In a small saucepan, bring the apricot, water, granulated sugar, brown sugar, and vanilla extract to a boil over medium heat, then reduce the heat to low and allow to simmer for about 10-15 minutes, or until the liquid has reduced by half and is mostly jammy in texture.

While it is simmering, heat the butter in a small frying pan over medium heat until it starts to turn amber colored and smells nutty. Remove it from heat as soon as this happens, if you leave it too long past that point it will burn.

Immediately mix together the brown butter, cream, milk, and salt in a medium saucepan over medium low heat until begins to bubble slightly around the edge. Slowly add some of the milk mixture to the eggs in the bowl, whisking constantly, until half of the milk mixture has been incorporated into the bowl. Pour the egg yolk mixture back into the saucepan and place the saucepan over low heat. Add the apricot mixture and the dark chocolate and stir until the chocolate is completely melted. Evenly distribute the mixture between 6 small ramekins that have been placed on a lipped baking sheet. Pour water into the baking sheet, taking care not to splash any into the ramekins, until it is about 3/4-inch deep all around the pan. Cover the pan with a large sheet of tin foil and place it in the oven.

Allow it to bake for 45-50 minutes, or until the caramel custard is set around the edges but still a bit wiggly in the center. Remove and allow to cool for 1 hour before serving. It can also be refrigerated for 4 hours and served chilled.