So no carbs pretty much at all. Difficult. Vegetables three times a week. Meat, eggs, hard cheese. Top chefs wouls struggle with only those ingredients. But it is something to play with. You could have cheese and ham omelette. Fried beef, stewed beef. It sounds bearable, just, like being on a constant no carbs diet. You'll have to be inventive with things like meat loaf, meat balls, liver, gravy soups. Then there is chicken. You didn't mention fish, which would be a great help. And then you have delicacies you could have, snail, jellied eels, mucus membrane soup, etc.
I know it must seem very boring to be so restricted, but frankly i think most people are bored with food even when they can eat anything. I was in a farmer's market today and there was wonderful foods all around, but I looked at each individually and none of them appetized me. So for my tea (5pm meal) I just had ham and cheese on toast, and even that I didn't finish. So remember you are not missing out very much if at all, effectively. Not as much as you might think.