too many hot chilli peppers in my Italian Beef!

The only things that could really work without modifying the recipe:

• pick out the peppers, if they're whole and not thoroughly cooked in
• add a lot more beef, so it's diluted down to a reasonable heat level

Otherwise, a couple options, which can be combined:

• add something creamy/fatty to cut the heat, e.g. sour cream, yogurt, coconut milk, or some kind of creamy sauce
• add enough of something else to get to a reasonable heat level, e.g. make a stew, make sandwiches with other ingredients, make pasta or rice, put it in baked potatoes, etc.

See also: How can you make a sauce less spicy/hot? and How can I wash down spicy food?

I have found that a slight amount of sugar put into chili can cut some of the heat, not enough to make it sweet, I usually add less than a teaspoon, however if you are talking spontaneous combustion level heat, I'm not so sure this solution would do you any good. I also concur with Jefromi and suggest that something creamy be added, hope this helps.

I had this problem once.

It turned out that the sauce was really spicy, but the meat itself was not spicy.

Remove the meat from the sauce and use another sauce for it; or adapt the meat to another recipe.