Mine are the exact opposite. Well, my younger is. My older is a human garbage disposal and will eat anything.
My younger will eat veggies by the armful, but only likes them raw. If they're cooked, in a sauce/dip, "hidden" in something which I've never believed in, or in another dish, forgettaboutit. I've had to tell her off for eating peas and string beans right off the plants so there's some left, but as soon as I saute them in butter and garlic, they may as well be old shoes and newspaper. She'll eat it if push comes to shove, but it's no work at all to simply leave things raw.
My method for getting my kids to try any new food is this: I wait until snack time. Get the new food, cut it up into small pieces with a bunch of other things - divided up of course, not all mixed- in bite-sized pieces. Some things they really, really like, a few things they like/are okay with and used to eating, and one or two things they're not comfortable with or haven't seen before. I set them on a big plate. And I leave.
There's no pressure to try, no comments if they don't, and no prep work involved for them. IME, if people of any age are comfortable with roughly 75% of the things on a plate, they're much more willing to try the thing they're uncomfortable with.
So for instance my youngest and pickiest might get a plate with grapes and mandarin slices (loves), granola bar bites and carrot rounds (likes), bits of salami (neutral on) and something she's never seen before, like our recent adventure with pineapple.
9 times out of 10, she'll try the unknown food, because the other food has served as a kind of primer that everything on that plate is "safe" and that I'm not giving her something horrible. That, combined with the no-pressure atmosphere and no consequence if she doesn't eat it, makes it very easy for her to try. She knows no one is going to stand over her and make her take x bites of it, or scold her, or hold it until the next meal until she gets too hungry and tries it out of desperation, or any of the other time-honored parenting tactics that have created a generation of wonderfully healthy eaters and healthy minds about food. (eyeroll) If she doesn't try it that time, oh well, it's just a small amoutn and I'll keep it off the snack plate for a few days/weeks then try it again. Eventually almost everything gets tried.