What is the ruling on eating food cooked with alcohol, and does the saying of the Prophet, peace and blessings be upon him, "That which intoxicates in large quantities is unlawful in small quantities," justify that if it does not lead to intoxication?

Every intoxicant is Khamr (wine), and every Khamr is unlawful. A small amount of it that intoxicates in large amounts is unlawful. So, every intoxicant is unlawful, and whatever intoxicates from it, a handful of it is unlawful, and a sip of it is unlawful. And the one who consumes food cooked with Khamr is consuming what is unlawful, and it contaminates the food, and consuming what is contaminated is unlawful.