I find that you can get this in some of the Davidoffs, AVO, Ashton and Fuente lines. Some amazing flavors that you can smoke on an empty stomach or in 90 degree heat without the nicotine crippling you. Just remember that what may be mild to one may be pretty strong to another.
BTW That is not a complete list of mild, full flavored cigars but just the lines that popped into my head. If you want to see this in all of it's glory then look into the world of Havanas.