In a double boiler or a heatproof bowl set over a pot of simmering water, add the semisweet chocolate chips. Stir occasionally until melted and smooth. Remove from heat and let it cool slightly.
In a mixing bowl, whisk together the egg yolks, granulated sugar, and a pinch of kosher salt until the mixture is pale and slightly thickened.
In a small saucepan, combine the whole milk and heavy cream. Heat over medium heat until the mixture is just about to simmer—do not let it boil.
Slowly pour the hot milk and cream mixture into the egg yolk mixture, whisking constantly to prevent the eggs from scrambling. This is called tempering.
Once combined, pour the egg and cream mixture back into the saucepan. Add the melted chocolate and vanilla extract, whisking until smooth.
Cook the mixture over medium-low heat, stirring constantly with a spatula, until it thickens slightly and coats the back of the spatula (about 5-7 minutes). Be careful not to let it boil.
Remove the custard from heat and strain it through a fine mesh strainer into a clean bowl to remove any lumps.
Pour the custard into ramekins or serving dishes. You can serve it warm immediately or cover it with plastic wrap and refrigerate for at least 2 hours to chill.