How to Make It
Combine ground coffee, salt, and sugar in large pot. Whisk to combine thoroughly, then whisk in half-and-half and first amount of heavy cream, making sure no coffee grounds are left clinging to side of pot.
Bring mixture to simmer (small bubbles begin to form around edges of pot) over medium high heat, stirring occasionally. Watch carefully—do not let it boil over. Once at a simmer, remove from heat.
Off heat, cover, and steep for EXACTLY 10 minutes. Set a timer.
Slowly pour the mixture through a fine strainer (or chinois) over a large bowl or pot. Press on the grounds with medium pressure using a wooden spoon or ladle to extract the liquid. Do not press too hard, or try to get every last drop of liquid through, as this will make the base taste bitter.
Add vanilla and instant espresso powder to mixture. Whisk or mix using an immersion blender until thoroughly combined. Chill until cool.
To make the ice cream base, combine milk, second amount of heavy cream, and second amount of sugar. Heat over medium heat, stirring regularly, until the mixture reaches a simmer. Remove from heat.
Place bowl over an ice bath (a large container or bowl filled with ice and just enough water for the ice to move around freely) and stir occasionally until cool.
Whisk ice cream base into second coffee mixture.
Freeze combined base according to your ice cream maker’s instructions.
While ice cream is still soft, fold in pieces of donuts. Do not overmix.
Let freeze until solid.