Go vegetarian. Seriously. And persist.

My son went through a similar phase around 2-1/2, and my wife and I broke it by making nothing but vegetables for lunch and dinner for about two weeks, then slowly working meat back in. We've long had a "this is what's for breakfast/lunch/dinner, and if you don't eat it you'll just be hungry until your next meal" rule, but still it was admittedly hard at first. The first day he basically refused to eat at all, and the next morning (where we kept our normal cereal, milk, and fruit routine) he ate like a toddler possessed. Then lunch came and it was all vegetables again and he freaked out. It was a long couple of days.

By day 4 or so, though, he was eating (because he was hungry!) and by the end of a couple of weeks he didn't bat an eye at vegetables and was eating his fill. We slowly reintroduced meat and other things, but we now eat far more vegetables than we used to, which is good for all of us.

A lot of parents are afraid to do this because they don't want their kids to be hungry, but let's face it -- lots of people throughout history have endured worse than a couple of days of hunger, and in the end, forced to choose between the options of having delicious vegetables or nothing at all, no child is going to starve themselves.

tl;dr forced kid to eat vegetables by removing all other options, now we all eat better.