In a medium saucepan, combine the cream, milk, sugar, Kahlua and espresso powder.
Bring to a gentle boil over medium heat. Remove from the heat.
In a medium bowl, beat the egg yolks until thickened.
Whisk 1 cup of the hot cream into the egg yolks.
Gradually add the egg mixture in a slow, steady stream, to the hot cream.
Cook over medium-low heat, stirring constantly, until the mixture thickens enough to coat the back of a spoon, about 5 minutes.
Remove from the heat and strain through a fine mesh strainer into a clean container.
Cover with plastic wrap, pressing down against the surface to keep a skin from forming.
Refrigerate until well chilled, at least 2 hours.
Remove from the refrigerator and pour into the bowl of an ice cream machine. Freeze according to the manufacturer's instructions. Transfer to an airtight container and freeze overnight until very firm.