Put sugar in a large 6 to 8-quart saucepan with a heavy bottom, and turn the heat to medium-high. Cook, occasionally shaking the pan but not stirring (you can scrape down the sides with a rubber spatula, but don’t stir the sugar itself) until the sugar liquefies, bubbles, and turns dark brown, at least 15 minutes. Turn off the heat, then carefully add the milk- very carefully, as it will bubble up, and this mixture is hot and sticky. Turn the heat to medium, and cook, stirring with a wire whisk, until the sugar dissolves; remove from heat.
Use an electric mixer to beat the egg yolks until they are light yellow. And thick. Pour about a third of the milk mixture into the egg mixture and stir, then pour that mixture back into the remaining milk mixture.
Cook over medium-low heat, stirring constantly, until the mixture reaches 175° to 180°, or is slightly thickened; do not boil. (There will be a thick coating on the back of the spoon, one that will hold the outline of your finger after you pass it through.) Cool over a bowl of ice, and then place in the refrigerator for about 4 hours until completely chilled.
Freeze the caramel custard in an ice cream machine, following manufacturer’s directions. You may add broken up crumbs of the beer brittle, or you may leave the ice cream simple as I have done, and serve it with beer brittle on the side and as a garnish.