In a large bowl, toss grated cheese with cornstarch. Set aside.
Seed and chop peppers, peel and chop onions. Peel and press or mince the garlic.
Put peppers, onion, and garlic, in food processor or blender, and let it rip till finely chopped.
In a medium sized saucepan, cook pepper mixture in olive oil until vegetables soften and the resulting liquid has cooked out.
Add beer and lime juice, continue cooking until it starts to simmer.
Add a good sized handful of cheese to the pot, and mix well till it is completely melted in.
Add another big handful, and repeat until all the cheese is added, completely melted, and smooth (aside from the pepper bits, of course!)
Transfer to fondue pot if desired, and serve with cubes of bread, tortilla chips, blanched broccoli, cauliflower, and asparagus, and slices of apples and pears.