Put the chocolate pieces in a large bowl and and set a mesh strainer over the top.
Warm the milk, sugar, and salt in a medium saucepan. In a separate medium bowl whisk together the egg yolks. Slowly pour the warm milk into the egg yolks, whisking constantly, then scrape the warmed egg yolks back into the saucepan.
Stir the mixture constantly over medium heat with a heatproof spatula, scraping the bottom as you stir, until the mixture thickens and coats the spatula. Pour the custard through the strainer over the white chocolate. Stir until white chocolate is completely melted and the mixture is smooth, then stir in the cream. Stir until cool over an ice bath.
Chill the mixture thoroughly in the refrigerator, then freeze it in your ice cream maker according to the manufacturer’s instructions.