Name the endpoint together
Ask each person what they expect to see when the cleanup is finished. One may expect dishes in the dishwasher and a wiped table. The other may also expect lunch portions put away and the sink available for breakfast. Write a short endpoint both people can recognize without having to inspect each other's work.
Assign the exception before leaving the room
If a pan needs attention later, say who will finish it and when. Fairness can vary across the week. Someone who cooked and cleaned on a late-shift night may want the other person to handle the whole dinner routine the following evening.
If a pan needs attention later, give that final step an owner and time. “Lee will finish the pan after the call and put it back” leaves the job visible. A vague remark that the pan can wait often means the next person in the kitchen inherits it unexpectedly.
Balance work across a whole week
Cooking can mean assembling sandwiches one night and preparing three dishes on another. Compare the effort, interruptions, and timing across several evenings instead of assuming that cooking and cleaning always weigh the same. When both people are tired, agree on the smaller cleanup needed tonight and the named work that can genuinely wait.