Every airline that I've every flown on allows people to bring food on board. As a courtesy to others, "fragrant" foods should be avoided.

When flying internationally to the US, plan to eat whatever you bring with you while you're on the flight into the US. Don't plan to save half for later. Skippy the Wonder Beagle, the dog which you may see at Baggage Claim or other areas, is an Agriculture Dog, not a DEA Dog. Skippy is looking for food - veggies, meats (sounds like sandwiches!), fruits, etc. in checked and carryon luggage.