I have the exact same problem. No matter how much butter and cheese I put on my vegetables, I still know they're there. I don't like to ruin my yummy meat dishes with vegetables in them.
What I do, is cook them and eat them with butter and eat them FIRST. Then as my reward (almost like dessert), I eat my meat plain. I still feel like I'm doing low-fat when I eat vegetables. I just can't find a way to disquise them.