boss, the owner, person in charge
闆 centers on a person in authority: a boss, owner, or the one in charge of a business or group.
闆 combines 門 (gate) with 品 (goods, items), likely suggesting a person overseeing goods or a business behind a gate. The exact historical development is uncertain, but the component combination fits the meaning of a boss or owner.
Inside the gate 門, three mouths 品 are talking at once. The boss is the one who manages all the chatter and keeps the business running.
For ハン, imagine the boss standing at the gate with a hand (ハン) raised, directing everyone inside: hand -> ハン, and the boss is in charge.