NOT A TEACHER
If I understand the information presented in English Grammar in Use correctly, it is often possible to use either the present simple or the present perfect after when, after, until and as soon as.
From English Grammar in Use, p. 50:
In your sentence, both "have" and "have had" are possible in my opinion.It is often possible to use either the present simple or present perfect:
I'll come as soon as I finish. or I'll come as soon as I've finished.
You'll feel better after you have something to eat. or You'll feel better after you've had something to eat.