Heat the half-and-half until it forms bubbles around the edge of the pan and steam starts to rise. Meanwhile, in the bowl of an electric mixer fitted with the paddle attachment, beat the egg yolks, sugar, and salt until mixed. Slowly add the hot half-and-half until combined. Wipe out the pan and pour the mixture back into the clean pan. Cook over medium-low heat, stirring constantly with a wooden spoon, for 5 to 10 minutes, until it's thickened and the cream coats the back of the spoon.
Pour the cream through a fine-meshed sieve into a bowl. Add the ground espresso beans, coffee liqueur, and vanilla and refrigerate until completely chilled.
Pour the espresso cream into an ice-cream freezer and freeze according to the manufacturer's directions. Mix in the chopped espresso beans, spoon into a container, and allow to freeze for a few hours. Soften slightly before serving.
