Add the milk, heavy cream, sugar, salt and black sesame paste into a medium saucepan and heat over medium-low heat until the sugar and black sesame are evenly dissolved and the milk starts to simmer and foam. Stir often with a whisk and make sure that the milk does not boil.
In a medium bowl, whisk the egg yolks.
Slowly add the milk mixture to the eggs, 1/2 cup at a time, whisking constantly to ensure that the eggs don't curdle.
Once the milk mixture is fully incorporated into the eggs, return the mixture to the saucepan and heat over medium heat. Continuously stir, until thickened.
Meanwhile, prepare an ice bath for a medium bowl.
Remove the saucepan from the heat and pour the black sesame mixture through a fine-mesh sieve into a medium bowl.
Place the bowl with the mixture into the ice bath.
When the mixture has cooled down, cover the bowl with plastic wrap and place in the refrigerator for at least 3 hours, or overnight if possible.