1530s, porage "thickened soup of vegetables boiled in water, with or without meat," an alteration of pottage, perhaps from influence of Middle English porray, porreie "leek broth," which is from Old French poree "leek soup," from Vulgar Latin *porrata, from Latin porrum "leek." Or perhaps the modern word is a corruption of porray itself, by influence of pottage.
The spelling with -idge is attested from c. 1600. The meaning "food made by slowly stirring meal or flour of oats, peas, etc. into water or milk while boiling till a thick mass is formed" is from 1640s, first in Scottish.