Whisk 1/2 cup of the whole milk with the cornstarch until completely smooth.
Combine the remaining whole milk, heavy cream, granulated sugar, espresso powder, and fine salt in a saucepan. Heat over medium heat until steaming but not boiling.
Whisk in the cornstarch mixture and cook, whisking constantly, until the custard thickens and bubbles gently. Continue cooking for 1 minute.
Remove the saucepan from the heat and add the chopped semisweet chocolate, butter, and vanilla extract. Let stand for 1 minute, then whisk until completely smooth and glossy.
Divide the chocolate custard among six small glasses or ramekins. Press parchment directly on the surface if you want to prevent a skin.
Refrigerate for at least 4 hours until cold and softly set. Let the pots de creme stand at room temperature for 10 minutes before serving for the creamiest texture.