Heat the milk, sugar, whole coffee bean, salt, and 1/2 cup (125 ml) of the cream in a medium saucepan until it is warm and steamy, but not boiling. Once the mixture is warm, cover, remove from the heat, and let steep at room temperature for 1 hour.
Reheat the coffee-infused milk mixture, on medium heat, until again hot and steamy, but not boiling. Pour the remaining 1 cup (250 ml) of cream into a medium size metal bowl, set on ice over a larger bowl. Set a mesh strainer on top of the bowl and set aside. In a separate medium bowl, whisk together the egg yolks. Slowly pour the warm coffee mixture into the egg yolks, whisking constantly so that the yolks are tempered by the warm milk, but not cooked by it. 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. This can take about 10 minutes. Pour the custard through the strainer and stir it into the ice bathed cream. Press on the coffee beans in the strainer to extract as much of the coffee flavor as possible, then discard the beans. Mix in the vanilla and the finely ground coffee and stir until cool over the ice bath.
Chill the mixture thoroughly in the refrigerator, then freeze it in your ice cream maker according to the manufacturer's instructions.