Anabanana is a great, cozy place. The owner cooks in her own kitchen and you're sitting in her dining room. She offers one daily menu which is mostly a mixed plate with one main and different small appetizers. Normally you can ask for for of the main if you're not filled up :) The food is delicious and I bet you'll find something you've never tried before. I think its all organic.
You can also order a starter and dessert. Its a bit pricey but in my opinion its worth it. When you live in Luxembourg or if you're here on a trip you should at least try Anabanana once. Especially when you're into discovering new things you'll like this heartwarming place :)
Be aware that you have to book a table (try via phone) because she only buys and cooks as much as she has booked tables.
Cons: not cheap