I enjoy the tasting menus as Asiatique, on Bardstown in Louisville. The chef does seperate seafood, meat and veggie tasting menus quite frequently (but call ahead to double check because it's not ALWAYS) and you can usually add a wine flight pairing as well.
1767 Bardstown Road, Louisville, KY 40208
Holly Hill Inn does a great tasting menu in Midway.
My other favorite is a tasting at Jonathans at Gratz Park.OH MY Goodness!
The Oakroom at The Seelbach in Lousiville used to do one but it has been awhile since I was there.
My cousin Loves the one at Jean Farris Winery but I havent been there, but we have the same taste.
Holly Hill Inn
426 N Winter St, Midway, KY 40347
Jean Farris Winery
6825 Old Richmond Road, Lexington, KY 40515
500 4th Avenue, Louisville, KY 40202
Limestone has a five course.
That was just by me searching real quick.
Here is a bit of advice, I have found by personal experience many restaurants are able and willing to create tasting menus if you call in advance. Now they have to be the kind of place that looks like you would expect to have one that maybe doesn't. It also helps if the chef is talented, local source driven, or up and coming.
I always use (which is true) I'm only going to have this one chance to try your restaurant while in town and would love a tasting menu. You would be amazed how many places will do this. Most Chefs are artists give them a challenge or a chance to spread their wings a bit, they will bite.
You will pay a bit more and it may just be a progression from the main menu at smaller portions but that in part is the point to get a feel for the Chef and His/Her creations.