They say pepperish, which is an expression alien to the English lexicon. The correct term is peppery – not pepperish. Note that the same thing applies to trickish, with the acceptable adjective from trick' being tricky: I didn't enjoy the meal because the soup was pepperish.
What's the meaning of Pepperish?
adjective. Resembling or redolent of pepper; peppery. Also figurative: irritable, testy, angry.
Does spicy mean peppery?
As to the original question: I would only use "peppery" to describe a food with a strong taste of black pepper. Other spices, such as chili* peppers, would make it "hot" or "spicy."