Melt butter in 1 1/2-2 quart flameproof fondue pot over medium-low heat. Add onion and garlic and cook, stirring occasionally, until completely soft and beginning to carmelize, about 15-20 minutes.
Meanwhile, in a large bowl, toss all three cheeses with cornstarch, mustard, and pepper.
Add caraway seeds to fondue pot and stir to toast them slightly, about 2 minutes. Add beer, and bring to a boil. Reduce heat to medium low and simmer to mellow the flavor of the beer, about 3 minutes.
Sprinkle the cheese mixture into the pot a large handful at a time, stirring each batch in a back and forth manner so that the cheese doesn't ball up as it melts. COntinue adding and stirring until all the cheese is melted, smooth, and thick, adjusting heat as necessary to maintain barely a simmer. Stir in sherry and season with salt.
Set fondue pot over a low flame at table to keep warm. Stir frequently and serve with dippers such as sourdough bread cubes, pear and apple slices, steamed carrots and cauliflower, boiled fingerling potatoes, grilled sliced sausage.