This would be a great concept for a theme restaurant. Cheese is an essential ingredient of many dishes and deserts (don't forget cheesecakes!). You can built your menu around a few cheese staples, such as pizza, calzones and lasagna, but be prepared to impress your patrons with a wide selection of cheese, served on platters. You can also serve cheese-bread before the meal.
Chances are, people will end up liking a couple of your carefully selected items, so you can sell them at a gift shop. Cheese lasts a long time, so you will never have problems with inventory, even if you choose to carry a couple very expensive imported cheeses. There are thousands of kinds of cheese available world-wide. When it comes to decorating the restaurant, you can use vintage cheese production tools, old packaging and some whimsical farm animals (cows, goats, sheep) to make the kids happy. White, yellow and green would be an easy choice for uniforms and even furniture.
P.S. Still looking for an actual restaurant that has already implemented this idea. Let me know if you find one!