With my Petersons i simply leave them to cool, maybe have a quick wipe of the bowl, and remove the stem the next day, so a i can clean the trap as well. The draw hole is near the bowl, and the trap behind it (if that makes sense).
If it's a P-lip mouthpiece get a fine pipecleaner, or if you haven't got one, clean as far as you can up the stem, remove, and blow to remove any debris. Repeat as needed.
If it's a P-lip mouthpiece get a fine pipecleaner, or if you haven't got one, clean as far as you can up the stem, remove, and blow to remove any debris. Repeat as needed.