Yes there's definitely that hunger window, that's when my DD actually eats cooked carrots.

In find she eats well when the veggies are soft and in a sauce, like a casserole. I squish it into the rice. Eggplant is great for this, even beans. Sometimes she eats raw mushroom pieces while I'm cutting them.
My DD also loves pumpklin soup or lentil soup, it's the novelty of dunking the bread in that makes it fun for her. And you can obviously puree anything into the soup.