In a medium saucepan, combine the milk, 1 ¼ cups of the cream, and the beans. Heat over medium heat until bubbles form around the edge of the pan. Do not boil. Remove from heat and cool to room temperature. Cover and refrigerate overnight in the saucepan. Once or twice during refrigeration, use a wooden spoon to break up the “crust” that forms on the surface and stir the beans back into the liquid.
The following day, put the remaining 1 cup cream in a large bowl set in an ice water bath. Place a fine mesh sieve over the bowl.
Warm the coffee bean mixture over low heat and strain it into a large measuring cup, pressing on the beans to extract as much liquid as possible. Add enough half-and-half to bring the liquid volume to 2 cups. Discard the beans and pour the liquid back into the saucepan. (Reserve the remaining half-and-half for another purpose.)
Place the egg yolks, sugar, and salt in the bowl of a food processor. Process until smooth and thick, 1 to 2 minutes.
Heat the coffee mixture over medium heat until bubbles appear around the edge of the pan. Do not boil. With the food processor running, gradually add the warm liquid to the egg mixture through the chute. Return the mixture to the saucepan.
Cook over medium heat, stirring constantly, until the mixture thickens and coats the back of a spoon (170 to 175 degrees F.) Pour through the sieve into the bowl and blend with the cream. Stir until slightly cooled and whisk in the vanilla and the ground coffee. Stir occasionally until cool and refrigerate until thoroughly chilled. (May be refrigerated overnight.)
Transfer the custard to an ice cream maker and freeze according to manufacturer’s instructions.