Make sure to take the cheeses and butter out of the fridge to soften at least 1 hour before preparing the dip.
Grind the caraway seeds in a food processor / coffee grinder / using a mortar and pestle. Finely chop chives and onion. Rinse the onion in a sieve.
Cut Camembert into cubes and add to a large bowl. Add melting cheese, butter, paprika, ground caraway seeds, and cayenne. Mash the mixture with a fork (pastry cutter also works well) until just slightly chunky but mostly smooth.
Add chopped chives, chopped and rinsed onion, and beer. Season to taste with salt and pepper, stir until combined.