The phrase "a menu on which" is correct and usable in written English.
It can be used when referring to a specific menu that serves as a basis for selection or choice, often in the context of food or options available.
Example: "The restaurant offers a menu on which customers can choose from a variety of gourmet dishes."
Alternatives: "a menu that features" or "a menu listing".
What else can one expect from a menu on which the largest item is quail?
This is a menu on which delicate squash blossoms appear only to be fried and stuffed with pulled pork.
Diners can pick entrees from a menu on which nothing costs more than $10, said the owner, Bob Tyler.
The Sugar House, which at the time had a menu on which every drink was keyed to a particular moment during Prohibition, served a drink called A Machine Gun Is the Last Word, combining barreled gin, Cardamaro, Aperol and lemon in a Chartreuse-rinsed glass (which, given its resemblance to a Paper Plane, probably makes it a riff on a riff).
They're most certainly not doing bar food, not with a menu on which the half dozen appetizers are easily outnumbered by the pasta dishes and main courses, not when the lasagna, made with braised lamb shoulder, is sculptured into a perfectly round and tidily layered cake that's like a prim haircut you itch to muss.
But read through this restaurant's menu, on which one fanciful mussel dish leads to another and then another after that, and you realize that its name is actually a truncated manifesto, a decree of intent, which is to show off mussels as they've never been shown off before.
Kimpton hotels recently rolled out a Travel Healthy menu, on which all choices are under 500 calories.
"These are Wichita prices!" said my friend from the Paris of the Plains, staring in awe at the menu, on which a double cheeseburger 'n fries was priced at $3.99.
Returned looking apologetic and held before her gaze back of menu on which was written "Party of Elks on way to World's Fair".
Prices for the specials are not mentioned, which might lead you to think that they are as reasonable as the printed menu, on which the top main course is grilled steak at $20.
The geographic breadth of its frequently changing menu, on which the prices of most entrees hover just above $20, prevents it from feeling as slight as it otherwise might.
