Would the barbecue of mice become barbecue?

The phrase "barbecue of mice" suggests a hypothetical scenario in which mice are being barbecued. If mice were to be cooked in such a manner, the resulting dish would likely be referred to as "barbecued mice" rather than simply "barbecue." The term "barbecue" typically denotes a cooking method or a gathering centered around grilled food, rather than a specific type of dish.