In a large bow, whisk eggs until they’re light and fluffy, about two minutes. Add both sugars a little bit at a time, whisking as you go, until they're well blended.
Add the milk and cream to the egg mixture and continue whisking to combine. Stir in beer.
Cover bowl and chill mixture in the fridge for at least 5 hours.
Add chilled mixture to ice cream machine and process according to manufacturer's instructions. Because there's alcohol in this ice cream, it will likely take longer to process and thicken.
Once thickened, transfer to airtight containers and place in freezer for another 5 hours so ice cream can continue to harden.
Scoop and serve! Sprinkle with chocolate shavings, if desired.